This monograph contains a proof of the Bestvina-Handel Theorem (for any automorphism of a free group of rank n, the fixed group has rank at most n) that to date has not been available in book form. The account is self contained, simplified, purely algebraic, and extends the results to an arbitrary family of injective endomorphisms. The topological proof by Bestvina Handel is translated into the language of groupoids, and many details previously left to the reader are meticulously verified in this text.