Lecture 1: A bridge between graph theory and additive combinatorics Lecture 2: Forbidding a Subgraph I: Mantel’s Theorem and Turán’s Theorem Lecture 3: Forbidding a Subgraph II: Complete Bipartite Subgraph Lecture 4: Forbidding a Subgraph III: Algebraic Constructions Lecture 5: Forbidding a Subgraph IV: Dependent Random Choice Lecture 6: Szemerédi’s Graph Regularity Lemma I: Statement and Proof Lecture 7: Szemerédi’s Graph Regularity Lemma II: Triangle Removal Lemma Lecture 8: Szemerédi’s Graph Regularity Lemma III: Further Applications Lecture 9: Szemerédi’s Graph Regularity Lemma IV: Induced Removal Lemma Lecture 10: Szemerédi’s Graph Regularity Lemma V: Hypergraph Removal and Spectral Proof Lecture 11: Pseudorandom Graphs I: Quasirandomness Lecture 12: Pseudorandom Graphs II: Second Eigenvalue Lecture 13: Sparse Regularity and the Green-Tao Theorem Lecture 14: Graph Limits I: Introduction Lecture 15: Graph Limits II: Regularity and Counting Lecture 16: Graph Limits III: Compactness and Applications Lecture 17: Graph Limits IV: Inequalities between Subgraph Densities Lecture 18: Roth’s Theorem I: Fourier Analytic Proof over Finite Field Lecture 19: Roth’s Theorem II: Fourier Analytic Proof in the Integers Lecture 20: Roth’s Theorem III: Polynomial Method and Arithmetic Regularity Lecture 21: Structure of Set Addition I: Introduction to Freiman’s Theorem Lecture 22: Structure of Set Addition II: Groups of Bounded Exponent and Modeling Lemma Lecture 23: Structure of Set Addition III: Bogolyubov’s Lemma and the Geometry of Numbers Lecture 24: Structure of Set Addition IV: Proof of Freiman’s Theorem Lecture 25: Structure of Set Addition V: Additive Energy and Balog-Szemerédi-Gowers Theorem Lecture 26: Sum-Product Problem and Incidence Geometry