Homotopy theory and C* algebras are central topics in contemporary
mathematics. This book introduces a modern homotopy theory for
C*-algebras. One basic idea of the setup is to merge C*-algebras
and spaces studied in algebraic topology into one category
comprising C*-spaces. These objects are suitable fodder for
standard homotopy theoretic moves, leading to unstable and stable
model structures. With the foundations in place one is led to
natural definitions of invariants for C*-spaces such as homology
and cohomology theories, K-theory and zeta-functions. The text is
largely self-contained. It serves a wide audience of graduate
students and researchers interested in C*-algebras, homotopy theory
and applications.
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