Though he is always called "John of Gaunt", it is a name he was never called in his own lifetime after the age of three when he received his first title. Gaunt is an English version Ghent where he was born.
Married:1st - Blanche of Lancaster, daughter of Henry of Grossmont, 1st Duke of Lancaster, on 19 May 1359 at Reading Abbey in Reading, Berkshire, England. 
Children of John of Gaunt and Blanche of Lancaster:
Philippa, Queen of Portugal.
Elizabeth, Duchess of Exeter. She married 1st John Hastings 2nd John Holland, 1st Duke of Exeter; 3rd Sir John Cornwall, 1st Baron Fanhope and Millbrook.
Henry IV of England
Married:2nd - Constance of Castile-León, daughter of Pedro the Cruel, King of Castile and León, before 29 September 1371 at Roquefort near Bordeaux, France. John of Gaunt would assume the title of King of Castile and León in right of his wife. She died 24 March 1394.
Children of John of Gaunt and Constance of Castile:
Catherine m. Henry III, King of Castile
Married:3rd - John of Gaunt had a well-known illicit relationship with Katherine de Roet, a governess of his children which began around 1372. She was the widow of Hugh de Swynford, knt. of Kettlethorpe and Coleby, Lincolnshire (d. 13 November 1371). They had 4 children born out of wedlock. On 13 January 1395/6, they were married at Lincoln Cathedral in Lincoln, Lincolnshore, England. A papal dispensation was received for this marriage on 1 September 1396. Their children were legitimized by parliament on 9 February 1397/8. 
Children of John of Gaunt and Katherine de Roet:
John Beaufort, 1st Earl of Somerset m. Margaret Holland
Cardinal Henry Beaufort
Thomas Beaufort, Duke of Exeter m. Margaret Neville
Died: 3 February 1399 at Leicester Castle in Leicester, Leicestershire, England. 
Buried: 15 March 1399 at St Paul's Cathedral in London, England.
From: Royal Tombs of Medieval England. "The fourth son of Edward III and Philipp of Hainault, John of Gaunt married Blanche, daughter and heiress of Henry of Grosmont, Duke of Lancaster, in 1360. She died on 12 September 1368 and was buried north of the choir in the cathedral church of St. Paul's London. Gaunt married Constance of Castile two years after Blanche's death. Gaunt died at Leicester Castle on 3 February 1399. The duke's will, dated the day of his death, instructed that his body was not to be embalmed and should remain unburied for forty days. It was to lie overnight at the Carmelite church on Fleet Street before interment near the high altar of St. Paul's beside Blanche. The year before his death, Gaunt had founded a chantry for himself and his third wife, Katherine Swynford, at Lincoln, and his will endowed two further chantries for himself and his first two wives at St. Paul's (Blanche) and the Church of the Annunciation of St. Mary in the Newarke at Leicester (Constance of Castile). Gaunt's body was taken from Leicester to London, stopping at St. Albans where a Requiem Mass was sung in the presence of Henry Beaufort. The duke was duly buried at St. Paul's on Passion Sunday, 16 March 1399, forty days after his death. His tomb was described at the time as 'sepultura incomparabile'. The tombs of the duke and his duchess Blanche both had effigies. The St. Paul's tombs and chantry were destroyed during the Great London Fire of 1666." 
↑ Cokayne. Complete Peerage, Lancaster: vol. VII p. 411-416.
↑ 11.011.111.2 John Cannon & Ralph Griffiths, The Oxford Illustrated History of the British Monarchy (University of Oxford, Great Clarendon Street, Oxford OX26DP, England: Oxford University Press, 2000), Genealogies of Royal Lines
↑ 12.012.112.212.3 Alison Weir, Mistress of the Monarchy: The Life of Katherine Swynford, Duchess of Lancaster (New York, NY: Randon House Publishing Group, 2010), Pages 35-36, 276
↑ 13.013.1 Norman F. Cantor, The Last Knight, (1230 Avenue of the Americas, New York, NY 10020: Simon & Schuster, Inc, 2004) Pages 1, 65, 71, 88, 195.
↑ 14.014.1 Allison Weir, The Wars of the Roses ; Ballantine Books, July 1996, Page 24
↑ 15.015.1 Alison Weir, The Princes in the Tower, Ballantine Books, August 1995, Page 260
↑ 16.016.1 Dan Jonew, The Plantagenets: The Warrior Kings and Queens Who Made England (New York, NY 10014: Viking Books, A Penguin Random House Company, 2012), Pages 375, 487
↑ Father: Henry, Duke of Lancaster; when Henry died, John became duke; d. dec. 1369
Weir, Alison. Katherine Swynford: The Story of John of Gaunt and his Scandalous Duchess. (London: Vintage Books. E-book, 2008).
Dan Jonew, The Plantagenets: The Warrior Kings and Queens Who Made England (New York, NY 10014: Viking Books, A Penguin Random House Company, 2012), Page 375
Weis, F.L. (1999). Magna Charta Sureties 1215, Frederick Lewis Weis, (5th ed).
John Cannon & Ralph Griffiths, The Oxford Illustrated History of the British Monarchy (University of Oxford, Great Clarendon Street, Oxford OX26DP, England: Oxford University Press, 2000), Genealogies of Royal Lines
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It may be possible to confirm family relationships with John by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree:
Accprding to relationship finder, he is my 16th great grandfather through his son John Beaufort and his granddaughter Joan Beaufort. However, relationship finder shows no relationship between me and Katehrine de Swynford, wife of John and mother of John Beaufort. How can this be?