Description: Based on a series of lectures delivered by the author at Moscow National University, and translated from the first (1947) Russian edition, this concise and rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Its lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete, careful and elegant manner. In addition to its value as text for a graduate-level course, this book can be used as a reference in preparing for seminars or examinations and as a source of basic information on combinatorial topology. "This little book, " reports The Mathematical Gazette, "is an extremely valuable addition to the literature of algebraic topology."

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