His name in Latin was Flavius Magnus Maximus Augustus
He went by Magnus Maximus.
His Brythonic/Welsh name was Macsen Wledig: Macsen the Emperor. 
335 Birth in Gallaecia
Maximus was born c. 335 in Hispania Gallaecia, on the estates of his uncle, Count Theodosius (the Elder), and Flavius Iulius Eucherius to whom he was the son, and Marcellinus, his brother. Near contemporaries described his dignity as offended when lesser men were promoted to high positions. 
David Peate has developed the hypothesis that Maximus was the grandson of a Spaniard who had earned the military title of Protector and the son of Iolinus, who was also Protector. 
Marriage and Issue
Cawley reports that the name of Maximus´s wife is not known. 
Maximus' wife was recorded having sought spiritual counsel from St. Martin of Tours during his time at Trier. Her fate and name have not been preserved in definitive historic records. The same is true of Maximus' mother and daughters, other than that they were spared by Theodosius I.
368 Junior Officer, Britain
Maximus may have been a junior officer in Britain in 368, during the quelling of the Great Conspiracy. 
373 Military Service in Africa
Maximus served under Count Theodosius in Africa in 373 
Maximus was assigned to Britain in 380 and defeated an incursion of the Picts and Scots in 381.
383 Usurps throne
In 383, as commander of Britain, he usurped the throne against the western emperor Gratian, who had become unpopular because of perceived favouritism toward Alans over Roman citizens. 
Proclaimed emperor by his troops, he went to Gaul to pursue his imperial ambitions, taking a large portion of the British garrison troops with him.
From Gaul, Maximus went out to meet Gratian, whom he defeated near Paris. Continuing his campaign into Italy, Maximus was stopped from overthrowing Valentinian II, who was only twelve, when Theodosius I, the Eastern Roman Emperor, sent Flavius Bauto with a powerful force to stop him.
384 Recognized as Augustus in the West
Negotiations followed in 384 including the intervention of Ambrose, Bishop of Milan, leading to an accord with Valentinian II and Theodosius I in which Maximus was recognized as Augustus in the west and emperor in Britannia and Gaul, while Gratian's brother Valentinian II retained Italy, Pannonia, Hispania, and Africa. 
Maximus made his capital at Augusta Treverorum (Treves, Trier) in Gaul, and ruled Britain, Gaul, Spain and Africa. He issued coinage and a number of edicts reorganizing Gaul's system of provinces. Some scholars believe Maximus may have founded the office of the Comes Britanniarum as well. 
He became a popular emperor; Quintus Aurelius Symmachus delivered a panegyric on Maximus' virtues. He used foederati forces such as the Alamanni to great effect. 
Maximus also established a military base in his native Gallaecia, i.e. Galicia (Spain), which persisted as a cultural entity despite occupation by the Suebi in 409, see Kingdom of Galicia. This kingdom successfully resisted the Moors and subsequently initiated the Spanish Reconquista. 
Power Transfer in Britain
Maximus' bid for imperial power in 383 coincides with the last date for any evidence of a Roman military presence in Wales, the western Pennines, and the fortress of Deva. Coins dated later than 383 have been found in excavations along Hadrian's Wall, suggesting that troops were not stripped from it, as was once thought. 
In the De Excidio et Conquestu Britanniae written c. 540, Gildas says that Maximus left Britain not only with all of its Roman troops, but also with all of its armed bands, governors, and the flower of its youth, never to return.
Having left with the troops and senior administrators, and planning to continue as the ruler of Britain in the future, his practical course was to transfer local authority to local rulers. 
After he became emperor of the Western Roman Empire, Maximus would return to Britain to campaign against the Picts and Scots (i.e., Irish), probably in support of Rome's long-standing allies the Damnonii, Votadini, and Novantae (all located in modern Scotland). While there he likely made similar arrangements for a formal transfer of authority to local chiefs—the later rulers of Galloway, home to the Novantae, would claim Maximus as the founder of their line, the same as did the Welsh kings.
387 Invasian of Italy
In 387, Maximus' ambitions led him to invade Italy. Forced out of Milan, emperor Valentinian II fled to Theodosius. Theodosious and Valentinian then invaded from the east and battled Maximus in July-August 388. Maximus was defeated by Theodosius I at the Battle of the Save in 388  and retreated to Aquileia. Meanwhile, the Franks under Marcomer had taken the opportunity to invade northern Gaul, at the same time further weakening Maximus' position.
Andragathius, magister equitum of Maximus and the killer of emperor Gratian, was defeated near Siscia while Maximus' brother, Marcellinus, fell in battle at Poetovio. 
Maximus surrendered in Aquileia, and although he pleaded for mercy was executed.  He was killed in 388 in Aquileia,  a city in the Western Roman Empire that is now in north east Italy. The Chronicle of Marcellinus records that Emperor Theodosius (of the Eastern Roman Empire) and his brother Valentinianus Gratiana defeated the "High Imposter and his sons" ("Maximum tyrannum et Victorem filius eius")  The Chronicon of Bishop Idatius records the same, adding that the month was V Kal Aug,  or August 28,, 388.
The Senate passed a decree of Damnatio memoriae against him. However, his mother and at least two daughters were spared. 
Theodosius' trusted general Arbogast strangled Maximus' son, Flavius Victor, at Trier in the fall of the same year. 
In the view of some historians, his death marked the end of direct imperial presence in Northern Gaul and Britain.
After Magnus' death in 388, the remains of his forces fled to Armorica.  Armorica is the portion of modern-day northwest France that includes Brittainy. 
Magnus is known to have had a wife: she is recorded as having sought spiritual counsel from St. Martin of Tours during his time at Trier. The name of Magnus' wife has not been preserved in historic records, nor her ultimate fate. 
All that is known of Maximus' mother and daughters is that they were spared by Theodosius I.
Wikipedia reports that one of Maximus' daughters may have been married to Ennodius, proconsul Africae (395); Ennodius' grandson was Petronius Maximus, another ill-fated emperor, who ruled in Rome for but 77 days before he was stoned to death while fleeing from the Vandals on May 24, 455. 
Other descendants of Ennodius, and thus possibly of Maximus, included Anicius Olybrius, emperor in 472, but also several consuls and bishops such as St. Magnus Felix Ennodius (Bishop of Pavia c. 514-21). 
In addition to these family members, there is Sevira, an otherwise unrecorded daughter of Magnus Maximus, who is named on the Pillar of Eliseg, an early medieval inscribed stone in Wales which claims her marriage to Vortigern, king of the Britons.
Biography: In Legend
Because the Saxons drove the Britons west into Cornwall and Wales, it is in the memories of those places that Maximus is recalled not only as a Roman emperor but as a "founding father." In fact he is shown as the "founding father" of several medieval Welsh kingdoms, including those of Powys and Gwent. He is given as the ancestor of a Welsh king on the Pillar of Eliseg, near Llangolen in northern Wales, erected nearly 500 years after he left Britain, and figures in lists of the Fifteen Tribes of Wales.
Boyer notes that of the legendary lines, that of Macsen Wledig is one of the most interesting and cannot be discarded without comment. Boyer presents material developed by David Peate as a hypothesis derived in part from the works of Bede, and Geoffrey of Monmouth as well as Eliseg's Pillar near Llangollen, which was transcribed by Edward Llwyd in 1696, and the Anglo-Saxon Chronicles. 
"Nennius" Historia Brittonum
The ninth century Historia Brittonum gives another account of Maximus and assigns him an important role: 
Warriors Taken from Britain. Maximianus, the seventh emperor, withdrew from Britain with all its military force, slew Gratianus the king of the Romans, and obtained the sovereignty of all Europe. Unwilling to send back his warlike companions to their wives, families, and possessions in Britain, he conferred upon them numerous districts from the lake on the summit of Mons Iovis, to the city called Cant Guic, and to the western Tumulus, that is Cruc Occident. These are the Armoric Britons, and they remain there to the present day.
Modern historians believe that this idea of mass British troop settlement in Brittany by Maximus may very well reflect some reality, as it accords with archaeological and other historical evidence and later Breton traditions. Armorica declared independence from the Roman Empire in 407 CE, but contributed archers for Flavius Aetius's defence against Attila the Hun, and its king Riothamus was subsequently mentioned in contemporary documents as an ally of Rome's against the Goths. Despite its continued usage of two distinct languages, Breton and Gallo, and extensive invasions and conquests by Franks and Vikings, Armorica retained considerable cultural cohesion into the 13th century.
Consequence: Britain Overrun. In consequence of their absence, Britain being overcome by foreign nations, the lawful heirs were cast out, till God interposed with his assistance.
Boyer reports the legend that Macsen married Elen Luyddog, the only daughter of Octavius (or Eudaf Hen -- cf Bartrum, 24), Duke of the Gewissi, who was in turn the son of Caradqwg, who was an ancestor of Conanus, of Cynan, King of Armorica. 
Dream of Macsen Wledig
Although the Mabinogion tale Breuddwyd Macsen Wledig (English: The Dream of Emperor Maximus) is written in later manuscripts than Geoffrey's version, the two accounts are so different that scholars agree the Dream cannot be based purely on Geoffrey's version. The Dream's account also seems to accord better with details in the Triads, so it perhaps reflects an earlier tradition. 
The Maiden. Macsen Wledig, the Emperor of Rome, dreams one night of a lovely maiden in a wonderful, far-off land. Awakening, he sends his men all over the earth in search of her. With much difficulty they find her in a rich castle in Wales, daughter of a chieftain based at Segontium (Caernarfon), and lead the Emperor to her. Everything he finds is exactly as in his dream. The maiden, whose name is Helen or Elen, 
accepts and loves him. Because Elen is found a virgin, Macsen gives her father sovereignty over the island of Britain and orders three castles built for his bride. 
Exile and Recovery. In Macsen's absence, a new emperor seizes power and warns him not to return. With the help of men from Britain led by Elen's brother Conanus (Welsh: Cynan Meriadoc, Breton: Conan Meriadeg), Macsen marches across Gaul and Italy and recaptures Rome. 
Brittany. In gratitude to his British allies, Macsen rewards them with a portion of Gaul that becomes known as Brittany.
As a result of this marriage between Maximus and a British woman, British descendants are made probable, and Maximus is given sovereignty over Britain, which he is then able to formally transfer from Rome back to the Britons themselves.
Welsh Triads: Other Versions of the Macsen and Helen Narrative
Legendary versions of Maximus' career in which he marries the Welsh princess Elen may have circulated in popular tradition in Welsh-speaking areas from an early date. Although the story of Helen and Maximus's meeting is almost certainly fictional, there is some evidence for the basic claims.
He is certainly given a prominent place in the earliest version of the Welsh Triads which are believed to date from c. 1100 and which reflect far older traditions. Welsh poetry also frequently refers to Macsen as a figure of comparison with later Welsh leaders.
Geoffrey of Monmouth
In about 1136, Geoffrey of Monmouth's Historia Regum Britanniae appeared.
Considered to be largely fictional, it is the basis for many English and Welsh legends. Cite error 3; Invalid <ref> tag; invalid names, e.g. too many
Roman Senator and Welsh Descendant. Maximianus as he calls him, was a Roman senator, a nephew of Coel Hen through Coel's brother Ioelinus, and king of the Britons following the death of Eudaf Hen. Geoffrey writes this came about because Octavius wanted to wed his daughter to such a powerful half-Roman-half-Briton and to give the kingship of Britain, as a dowry, to that husband, so he sent a message to Rome offering his daughter to Maximian.
Caradocus, the Duke of Cornwall, had suggested and supported the marriage between Octavius's daughter and Maximian. Maximian accepted the offer and left Rome for Britain. 
Maximian's Invasian. Geoffrey claims further that Maximian gathered an army as he sacked Frankish towns along the way. He invaded Clausentum (modern Southampton) unintentionally and nearly fought the army of the Britons under Conan Meriadoc before agreeing to a truce. Following further negotiations, Maximian was given the kingship of Britain and Octavius retired. *Invasian of Gaul. Five years into his kingship, Magnus Maximus assembled a vast fleet and invaded Gaul, leaving Britain in the control of Caradocus. Upon reaching the kingdom of Armorica (historically, the region between the Loire and Seine rivers, later comprising Brittany, Normandy, Anjou, Maine and Touraine), he defeated the king and killed thousands of inhabitants. 
Founding of Brittany. Before departing to Rome, he summoned Conanus, the rebellious nephew of Octavius, and asked him to rule as king of the land, which was renamed Brittany, or "Little Britain". 
The tongues of Native Women. Conan's men married native women after cutting out their tongues to preserve the purity of their language. Geoffrey of Monmouth presents this legend to explain the Welsh name for Brittany, Llydaw, as originating from lled-taw or "half-silent". Given that Conan was well established in genealogies as the founder of Brittany, this account is certainly connected to an older tradition than Geoffrey. 
Gracianus Municeps. Following the death of Caradocus, rule of Britain as regent passed to Dionotus, who - facing a foreign invasion - appealed to Maximus, who finally sent a man named Gracianus Municeps with two legions to stop the attack. He killed many thousands before the invaders fled to Ireland. Maximus died in Rome soon after and Dionotus became the official king of the Britons. Unfortunately, before he could begin his reign, Gracianus took hold of the crown and made himself king over Dionotus. 
The prominent place of Macsen in history, Welsh legend and in the Matter of Britain means he is often a character or referred to in historical and Arthurian fiction. Such stories include 
Stephen R. Lawhead's Pendragon Cycle,
Mary Stewart's The Hollow Hills,
Jack Whyte's Camulod Chronicles,
M J Trow's Britannia series,
Nancy McKenzie's Queen of Camelot and
Rudyard Kipling's Puck of Pook's Hill.
The popular Welsh folk song Yma o Hyd, recorded by Dafydd Iwan in 1981, recalls Macsen Wledig and celebrates the continued survival of the Welsh people since his days.
Maximus in Welsh Genealogies
The earliest Welsh genealogies give Maximus (referred to as Macsen/Maxen Wledig, or Emperor Maximus) the role of founding father of the dynasties of several medieval Welsh kingdoms, including those of Powys and Gwent.
He is given as the ancestor of a Welsh king on the Pillar of Eliseg, erected nearly 500 years after he left Britain, and he figures in lists of the Fifteen Tribes of Wales.
Ancestor: Sextus Iulius Caesar
Grandfathers: Iulius Honorius / Marcus Aurelius Mausaeus Valerius Carausius
Father: Flavius Iulius Eucherius
Uncles: Flavius Iulius Theodosius / Flavius Iulius Honorius
Cousins: Flavius Theodosius / Flavius Honorius
Second Grade Nephews: Flavius Didimus / Flavius Theodosiolus / Flavius Lagodius / Flavius Verenianus / Flavius Honorius / Flavius Arcadius / Favia Serena / Flavia Maria / Galla Placidia
Wife: Helen ferch Eudaf
Sons: Flavius (Victor / Eugenius / Publicius / Antonius / Aldroenus /
Daughters: Flavia Severa / Flavia Aelia Flacilia
Grandsons: Flavius Constans / Flavius Ambrosius Aurelius) / Flavius Eucherius
Cawley, the most authoritative source, reports that Maximus & his wife had one child
Victor, who was killed in Gaul in 388. Cawley adds that "Zosimus records that Emperor Theodosius awarded "dignitate Cæsaris" to "Maximum…filium Victorem". The Chronicon of Bishop Idatius records that “filius Maximi…Victor” was killed in Gaul in 388 by “Arbogastem Comitem”. The Chronicle of Marcellinus records that "Valentinianus Gratiani frater et Theodosius imperatores" defeated the rebel "Maximum tyrannum et Victorem filius eius" at Aquileia in 388." 
Wikipedia provides two sons:
Flavius Victor birth year unknown; however, he assumed co-reign with father in 384. If he were 25 at the time, his birth year would have been about 359. He died in Trier August 388.
Unknown Theodosian birth year unknown. (possible) ___ dau. m. Ennodius. One dau may have married Ennodius, proconsul Africae. Ennodius' grandson was Petronius Maximus, another ill-fated emperor, who ruled in Rome for 77 days before ... he was stoned to death fleeing from the Vandals May 24, 455. Other descendants of Ennodius, and thus possibly of Maximus, included Anicius Olybrius, emperor in 472, but also several consuls and bishops such as St. Magnus Felix Ennodius (Bishop of Pavia c. 514-21).
The following substantially legendary line of descent is mostly derived from Historum Brittainorum, dated 828, so at its earliest it is reporting events 500 years earlier without further documentation. 
Emperor Magnus Maximus (c. 335-388) (? m. Helen)
Severa m. Vortigern, King of Britain (c. 370-c. 441)
Pascent, King of Buellt and Gwrtheyrnion (b. c. 410)
Riagath, King of Buellt and Gwrtheyrnion (b. c. 445)
Mepurit, King of Buellt and Gwrtheyrnion (b. c. 485)
Paul, King of Buellt and Gwrtheyrnion (b. c. 520)
Eldoc, King of Buellt and Gwrtheyrnion (b. c. 555)
Eldad, King of Buellt and Gwrtheyrnion (b. c. 590)
Moriud, King of Buellt and Gwrtheyrnion (b. c. 625)
Guoidcant, King of Buellt and Gwrtheyrnion (b. c. 660)
Pascent, King of Buellt and Gwrtheyrnion (b. c. 700)
Gloud (b. c. 735)
Brawstudd (b. c. 775) m. Arthfael, King of Glywysing (b. c. 765)
↑ Phillimore, Egerton, ed. (1887), "Pedigrees from Jesus College MS. 20", Y Cymmrodor, VIII, Honourable Society of Cymmrodorion, pp. 83–92 Cited at Wikipedia: Magnus Maximus
↑ Phillimore, Egerton (1888), "The Annales Cambriae and Old Welsh Genealogies, from Harleian MS. 3859", in Phillimore, Egerton, Y Cymmrodor, IX, Honourable Society of Cymmrodorion, pp. 141–183 Cited at Wikipedia: Magnus Maximus
↑ Rachel Bromwich, editor and translator. Trioedd Ynys Prydein: The Welsh Triads. Cardiff: University of Wales Press, Third Edition, 2006. 441-444 Cited at Wikipedia: Magnus Maximus
↑ Peate. West Saxons from Powys: A Hypothesis, 29. Cited by Boyer, 242
↑ otherwise unrecorded dau Magnus Maximus, Sevira, on Pillar of Eliseg, early medieval inscribed stone in Wales which claims her marriage to Vortigern, king of the Britons.
↑ In a discussion on the
Soc.Gen.Medieval List, Isla McDonald displayed a line of descent provided in Peter Bartrum's Welsh Genealogies AD 300-1500 , with dates adjusted by her. The descent in turn came from Historia Brittainorum (828). McDonald said that the first three generations could be deduced from the early accounts of Vortigern's family and the Pillar of Eliseg (9th century). Stewart Baldwin responded that "although Magnus Maximus was historical, and there is no good reason to doubt the existence of Vortigern, Helen is completely fictional, and Severa was probably also an early invention." Accessed Sept 6, 2017. jhd