This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.S. Mathematics Institute (JAMI). The book centers on the following: classical and nonclassical theory of $H$-spaces, compact groups, and finite groups, classical and chromatic homotopy theory and localization, classical and topological Hochschild cohomology, elliptic cohomology and its relation to Moonshine and topological modular forms, and motivic cohomology and Chow rings. It surveys the current state of research in homotopy theory and suggests a framework for future developments. The book begins with two historical accounts, of the work of Professors Peter Landweber and Stewart Priddy, in honor of their sixtieth birthdays.

Table of Contents:
Two papers on the history of topology: A marriage of manifolds and algebra: The mathematical work of Peter Landweber by H. Miller Some mathematical influences of Stewart Priddy by N. Minami Research papers: Some properties of the $K$-theory completion by M. Bendersky and R. D. Thompson Nonimmersions of real projective spaces implied by $tmf$ by R. R. Bruner, D. M. Davis, and M. Mahowald High Euler characteristics for almost extraspecial $p$-groups by M. Brunetti Unstable $p$-th order operation and $H$-spaces by Y. Hemmi The structure of 24 dimensional manifolds having normal bundles which lift to $BO[8]$ by M. Mahowald and M. Hopkins The homology of $BPO$ by P. Hu and I. Kriz $\mathcal{A}$-generators of the cohomology of the Steinberg summand $M(n)$ by M. Inoue Commutators in the homology of $H$-spaces by J. P. Lin A solution of Deligne's Hochschild cohomology conjecture by J. E. McClure and J. H. Smith Hopf algebra structure of Morava $K$-theory of the exceptional Lie groups by M. Mimura and T. Nishimoto Minami-Webb type decompositions for compact Lie groups by J. Martino and S. Priddy The method of infinite descent in stable homotopy theory I by D. C. Ravenel The homotopy groups $\pi_*(L_nT(m)\wedge V(n-2)$ by K. Shimomura The fiber of iterated Freudenthal suspension and Morava K-theory of $\Omega^kS^{2\ell+1}$ by D. Tamaki On $K$-flat and $K$-moonshine-like elements in elliptic cohomology by M. Tanabe The geometric fixed point spectrum of $({\mathbf Z}/p)^k$ Borel cohomology for $E_n$ and its completion by T. Torii A possible new approach to the motivic spectral sequence for algebraic K-theory by V. Voevodsky Rings of invariants and inseparable forms of algebras over the Steenrod algebra by C. W. Wilkerson, Jr. Chow rings of classifying spaces of extraspecial $p$ groups by N. Yagita.