Contents:
Smooth Morse Theory:
First Steps
Fundamental Results in Morse Theory
Topological Consequences
Homology
Piecewise Linear Morse Theory
Discrete Morse Theory:
First Steps
Topological Consequences
Algorithms
Applications
Appendices:
Smooth Manifolds
Cell Complexes

Morse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels between the two subjects. This is the first time both smooth and discrete Morse theory have been treated in a single volume. This makes the book a valuable resource for students and professionals working in topology and discrete mathematics. With a strong focus on examples, the text is suitable for advanced undergraduates or beginning graduate students.