This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in August 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: application of homotopy theory to group theory fiber bundle theory homotopy theory. The expository papers consider the following topics: the Atiyah-Jones conjecture (by C. Boyer) classifying spaces of finite groups (by J. Martino) instanton moduli spaces (by R. J. Milgram) Homotopy Theory and Its Applications. It offers a distinctive account of how homotopy-theoretic methods can be applied to a variety of interesting problems.