Lecture 1, Jan 9: Introduction, the first moment method. Chapters 1 and 2 from Alon & Spencer. Lecture 2, Jan 16: Alterations. Chapter 3 from Alon & Spencer Lecture 3, Jan 23: Local Lemma. Chapter 5 from Alon & Spencer Lecture 4, Jan 30: More on the Local Lemma Lecture 5, Feb 6: Concentration. Chapter 7 from Alon & Spencer, Chapters 10, 11 from Molloy & Reed Lecture 6, Feb 13: Total colouring; colouring graphs with girth 5. Chapters 7, 12 from Molloy & Reed Lecture 7, Feb 27: The List Colouring Conjecture. Chapter 14 from Molloy & Reed Lecture 8, Mar 6: Algorithms for the Local Lemma. Chapter 5 from Alon & Spencer Lecture 9, Mar 13: Triangle-free graphs. Lecture 10, Mar 20: List colouring bipartite graphs; Independence number of K_t-free graphs Lecture 11, Mar 27: More on the Local Lemma; R(k,k) Lecture 12, Apr 3: