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 offers a distinctive account of how homotopy-theoretic methods can be applied to a variety of interesting problems.

A. Adem -- Discrete groups, Grothendieck rings and families of finite subgroups 
Anonymous -- Once in class with Sam 
L. Astey -- Stably fibre homotopy invariant classes in complex-oriented theories 
D. J. Benson and C. W. Wilkerson -- Finite simple groups and Dickson invariants 
C. P. Boyer -- The Atiyah-Jones conjecture 
F. R. Cohen -- On combinatorial group theory in homotopy 
F. R. Cohen, J. R. Harper, and R. Levi -- On the homotopy theory associated to certain finite groups of $2$-rank two 
D. M. Davis -- Equivalences of some $upsilon _1$-telescopes 
J. Dietz and S. Priddy -- The stable homotopy type of rank two $p$-groups 
M. Mahowald and V. Gorbounov -- Some homotopy of the cobordism spectrum $MOlangle 8

angle$ 
I. M. James -- Numerical invariants of fibrewise homotopy type 
K. Y. Lam and D. Randall -- Geometric dimension of bundles on real projective spaces 
J. R. Martino -- Classifying spaces and their maps 
R. J. Milgram -- The Atiyah-Jones conjecture for ruled surfaces and the geometry of instanton moduli spaces 
E. G. Rees -- Linear spaces of real matrices of given rank 
J. Seade -- A note on the Adams $e$-invariant

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