Since the work of Stasheff and Sugawara in the 1960s on recognition of loop space structures on $H$-spaces, the notion of higher homotopies has grown to be a fundamental organizing principle in homotopy theory, differential graded homological algebra and even mathematical physics. This book presents the proceedings from a conference held on the occasion of Stasheff's 60th birthday at Vassar in June 1996. It offers a collection of very high quality papers and includes some fundamental essays on topics that open new areas. It's features include: accessible to a broad audience interested in mathematics and physics; offers a comprehensive overview of Stasheff's work; and, contains papers on very current research topics, including operads, combinatorial polyhedra and moduli spaces.

Table of Contents:
An appreciation of the work of Jim Stasheff by J. McCleary The cohomology flat product and the Berstein algebra of a co-H-space by M. Arkowitz and H. Scheerer Spaces of local vector fields by J. C. Becker and D. H. Gottlieb Operads from the viewpoint of categorical algebra by T. Beke Double loop spaces, braided monoidal categories and algebraic 3-type of space by C. Berger Poisson brackets with divergence terms in field theories: Three examples by L. A. Dickey Grassmannian and elliptic operators by L. Friedlander and A. Schwarz On the deformation of rings and algebras. V: Deformation of differential graded algebras by M. Gerstenhaber and C. W. Wilkerson Perturbation and transfer of generic algebraic structure by K. Hess Extensions of Lie-Rinehart algebras and the Chern-Weil construction by J. Huebschmann On the category of fibre bundles, Lie groups, and Frobenius maps by I. M. James and W. Singhof Hidden Stasheff polytopes in algebraic $K$-theory and in the space of Morse functions by M. M. Kapranov and M. Saito Commutators of $A_\infty$ structures by T. Lada Simplex, associahedron, and cyclohedron by M. Markl Rings of generalized and stable invariants and classifying spaces of compact Lie groups by F. Neumann, M. D. Neusel, and L. Smith Block bundle origin of stable block bundle homotopy by D. Randall On $p$-minimal homological models of twisted tensor products of elementary complexes localised over a prime by J. A. Armario, P. Real, and B. Silva Stability of the rational homotopy type of moduli spaces by A. A. Voronov.