My Great Grandfather, Augustus Alexander Muller/Mueller/Miller was born 24 September 1842 in Cologne, Germany to August Muller and Adelheid Schmitz. He moved to New Zealand approximately 1863, married my Great Grandmother in 1877. He was a cabinet maker, many of his descendants followed in that profession, so I can only assume that he learned the trade from his father.
All I really know about his parents is the following: August Muller born about 1825 in Germany, Adelheid Elisabeth Schmitz born about 1820-1825 in Germany. Married 20 April 1843 Godesberg, Rheinland, Prussia. They had a son 21 September (not sure of the year, the vital record did not show it), Hermann Joseph Mueller/Muller in Godesberg, Rheinland, Prussia. Another Son Augustus Alexander Mueller/Muller 24 September 1842, Cologne, Germany (died 20 October 1919, Footscray, Victoria, Australia)
August and Adelheid have been my "forever" brick wall. I have searched all over ancestry, my heritage, family search, and a smattering of "other" german sites. German research is so far out of my comfort zone that even if I was looking at the right records, I doubt I would even recognize it. Imagine a deer in the headlights, that's me trying to focus on German records.