This book is intended as a text for a one-year introductory course in abstract algebra, with an emphasis on certain algorithmic questions. It uses the APL programming language for examples and exercises, and it includes a description of APL and some special workspaces in a 70-page Appendix. The book is fairly traditional in scope; inclusion of factorization of polynomials over a finite field, multiple-precision arithmetic, and, as previously mentioned, APL, are distinguishing features. Applications of algebra or algebraic computing, such as coding theory or symbolic computation with formal power series, Newtown iteration, or the Chinese Remainder Algorithm, are not included.