"The First Muirs of The Province of Quebec" is the first professional research effort to identify all of the early Muir's who arrived after the French and Indian War which ended in 1763. Their origins and relationships are explored and parents identified for the first time for some of them. Evidence is presented herein that the Two Millers, James and William Muir, were brothers and were possibly related to Adam and Archibald Muir. James and William's Scottish origins were discovered as were their siblings. The Descendants of James Muir of Beloeil, Vercheres, Quebec, are documented through five generations to include all descendants that could be identified. Many of the spouses of these descendants and their parents were also identified for the first time. Many descendants migrated to Vermont, New Hampshire, Maine, Connecticut and Massachusetts to work in the mills that were springing up in the nineteenth century there. The variation of French names which changed from record to record as well as the French custom of "dit" names were major challenges that had to be overcome in this research.