This is the second volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include homotopy groups, fibre bundles, dynamical systems, and foliations. The exposition is simple and concrete, and in a terminology palatable to physicists.

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.
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

Bibliography
Index