Chapter 1: Examples of Manifolds.
Chapter 2: Foundational Questions. Essential Facts Concerning Functions on a Manifold. Typical Smooth Mappings.
Chapter 3: The Degree of a Mapping. The Intersection Index of Submanifolds. Applications.
Chapter 4: Orientability of Manifolds. The Fundamental Group. Covering Spaces (Fibre Bundles with Discrete Fibre).
Chapter 5: Homotopy Groups.
Chapter 6: Smooth Fibre Bundles.
Chapter 7: Some Examples of Dynamical Systems and Foliations on Manifolds.
Chapter 8: The Global Structure of Solutions of Higher-Dimensional Variational Problems.