The talk would describe the use of semidefinite programming in the development of approximation algorithms for combinatorial optimization problems. The talk would start with a definition of semidefinite programming. No prior knowledge of the subject would be assumed. It would then briefly cover Lovász’s ϑ-function, the MAX CUT approximation algorithm of Goemans and Williamson, the coloring algorithm of Karger, Motwani and Sudan, the MAX 3-SAT algorithm of Karloff and Zwick, and time permitting more modern developments.