This book describes fundamental groups and their topological soulmates, the covering spaces. An accomplished example of the algebraic topologist's dream come true, covering spaces are a geometric (that is, topological) structure that is completely characterized by its algebraic counterpart.

The author provides several illustrative examples that touch upon different areas of mathematics, but in keeping with the book's introductory aim, they are all quite elementary. Basic concepts are clearly defined, proofs are complete, and no results from the exercises are assumed in the text.

The elementary character of fundamental groups and covering spaces are presented as suitable for introducing algebraic topology. The two topics are treated in separate sections. The focus is on the use of algebraic invariants in topological problems. Applications to other areas of mathematics such as real analysis, complex variables, and differential geometry are also discussed.

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