Fundamental Groups and Covering Spaces
The book is an introduction to a part of algebraic topology. It concentrates on the circle of ideas around homotopy theory, fundamental groups and covering spaces. The first part of the book introduces a general concept of a homotopy, together with a particular case of path homotopy. The fundamental group is defined and computed for many examples, including real and complex projective spaces and classical matrix groups. The fundamental group of the circle is related to winding numbers of plane curves. The second part of the book is devoted to basic properties of (differentiable) covering spaces and their relations to fundamental groups. Each chapter ends with exercises. The book starts from the beginning and its reading requires only a basic knowledge. The book is a pleasure to read, it contains a lot of illustrations and presentation is clear and systematic.