Homology: Four Lectures — Budapest REU Math Program 2026

**Homology: Four Lectures — Budapest REU Math Program 2026**

This book is a reorganized and expanded collection of lecture notes based on four homology lectures that I attended during a small-group learning session at the Budapest REU Math Program 2026, within the research theme *Algebraic Curves: A Topological Perspective*.

The material introduces fundamental concepts in algebraic topology, including simplices, simplicial complexes, singular and simplicial homology, chain complexes, boundary operators, homotopy invariance, and applications of homology.

The original handwritten notes have been reorganized into a structured English-language learning resource, with additional explanations, mathematical examples, proofs, and illustrations to make the material easier to understand and review.

This book is intended for university students and mathematics enthusiasts interested in algebraic topology.

**Academic attribution:** The mathematical content is based on the four lectures attended during the Budapest REU Math Program 2026. Saran Phosuwan compiled, reorganized, and expanded the lecture notes for educational purposes.