The theory of generalized inverses of real or complex matrices is a well-developed and well-documented subject. However, the wider subject of generalized inverses of matrices over rings has reached a state for a comprehensive treatment only recently. The author, who contributed to this development, provides a book for students of the subject. Mathematicians working in g-inverses of matrices, algebraists and control theorists will be interested in the results presented here. The book would also be suitable for graduate courses on G-inverses in algebra.