Geometry and Topology of Manifolds

This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal.

Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We…