The group fixed by a family of injective endomorphisms of a free group

the long version

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.