# Lectures on Algebraic Topology

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*Sergey V. Matveev*

A publication of the European Mathematical Society

Algebraic topology is the study of the global properties of spaces by
means of algebra. It is an important branch of modern mathematics with a wide
degree of applicability to other fields, including geometric topology,
differential geometry, functional analysis, differential equations, algebraic
geometry, number theory, and theoretical physics.

This book provides an introduction to the basic concepts and methods of
algebraic topology for the beginner. It presents elements of both homology
theory and homotopy theory, and includes various applications.

The author's intention is to rely on the geometric approach by appealing to
the reader's own intuition to help understanding. The numerous illustrations in
the text also serve this purpose. Two features make the text different from the
standard literature: first, special attention is given to providing explicit
algorithms for calculating the homology groups and for manipulating the
fundamental groups. Second, the book contains many exercises, all of which are
supplied with hints or solutions. This makes the book suitable for both
classroom use and for independent study.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in geometry and topology