Serving as both a graduate textbook on Reimannian holonomy groups and a research monograph on the exceptional holonomy groups Gc and Spin(7), this book is intended for mathematicians working in differential and Riemannian geometry and physicists working in String Theory. It's overall subject is Riemannian manifolds with special holonomy groups, especially Ricci-flat holonomy groups SU(m), Sp(m), G2, and Spin(7). Constructions and existence theorems are emphasized. Most proofs are given in full.