Not merely an account of new results, this book is also a guide to motivation behind present work and potential future developments. Readers can obtain an overall understanding of the sorts of problems one studies in group actions and the methods used to study such problems. The book will be accessible to advanced graduate students who have had the equivalent of three semesters of graduate courses in topology; some previous acquaintance with the fundamentals of transformation groups is also highly desirable. The articles in this book are mainly based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado.A major objective was to provide an overall account of current knowledge in transformation groups; a number of survey articles describe the present state of the subject from several complementary perspectives. The book also contains some research articles, generally dealing with results presented at the conference. Finally, there is a discussion of current problems on group actions and an acknowledgement of the work and influence of D. Montgomery on the subject.

Table of Contents:
The work and influence of Deane Montgomery by F. Raymond and R. Schultz Bibliography of Deane Montgomery Homotopy-Theoretic Techniques and Applications: Homotopy invariants and $G$-manifolds: A look at the past fifteen years by R. Schultz Splitting semifree group actions on homotopy spheres into solid tori by R. Dotzel Equivariant Whitehead torsion and actions of compact Lie groups by S. Illman Homological Methods and Machinery: A family of unusual torus group actions by C. Allday For $G=S^1$ there is no $G$-Chern character by J.-P. Haeberly Equivariant frameability of homotopy linear $S^1$ actions on spheres by P. Loffler and R. Schultz Action maps on equivariant function spaces and applications to $PL$ bordism by B. M. Mann and E. Y. Miller Borsuk-Ulam theorems for prime periodic transformation groups by A. Necochea On equivariant maps of Stiefel manifolds by D. Randall Applications of Surgery and Geometric Topology: Representations at fixed points by S. Cappell and J. Shaneson Transformation groups and fixed point data by K. H. Dovermann, T. Petrie, and R. Schultz Lectures on transformation groups and Smith equivalence by M. Masuda and T. Petrie Transformation groups and exotic spheres by R. Schultz Constructions of group actions:A survey of recent developments by S. Weinberger Concordance of group actions on spheres by A. Assadi Induction in equivariant $K$-theory and $s$-Smith equivalence of representations by E. C. Cho and D. Y. Suh Smith equivalent representations of generalized quaternion groups by E. C. Cho $s$-Smith equivalent representations for finite abelian groups by D. Y. Suh Isotropy representations of nonabelian finite group actions by Y. D. Tsai Low-dimensional Topology and Transformation Groups: Transformation groups and low-dimensional manifolds by A. Edmonds Homogeneous Spaces and Seifert Fiberings: The role of Seifert fiber spaces in transformation groups by K. B. Lee and F. Raymond Realizing group automorphisms by D. Fried and R. Lee Cohomology of a Siegel modular variety of degree two by R. Lee and S. Weintraub Transformation Groups and Differential Geometry: Newman's theorem and the Hilbert-Smith conjecture by H. T. Ku, M. C. Ku, and L. N. Mann Geometry, representation theory, and the Yang-Mills functional by H. T. Laquer Problems: Problems submitted to the AMS Summer Research Conference on Group Actions by R. Schultz.