An Introduction to Morse Theory

This book introduces basic concepts related to finite dimensions, including critical points, the Hessian, and handle decompressions. It first uses surfaces to illustrate these ideas, and then generalizes them to apply to higher dimensions. This treatment then informs a discussion of handlebodies, homology, and low-dimensional manifold theory. 

Table of Contents

Chapter 1. Morse Theory on Surfaces

Chapter 2. Extension to General Dimensions 

Chapter 3. Handlebodies 

Chapter 4. Homology of Manifolds 

Chapter 5. Low-dimensional Manifolds