Introduces equivariant homotopy, homology, and cohomology theory, along with related issues in modern algebraic topology. The work begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. It then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. Finally, it gives an introduction to "brave new algebra." Annotation c. by Book News, Inc., Portland, Or.