Part I: General methodologies complexity and approximability polyhedral combinatorics branch-and-cut algorithms matroids and submodular functions advances in linear programming decomposition and column generation stochastic integer programming randomized algorithms local search graphs and matrices. Part II: Specific topics and applications sequencing and scheduling "Travelling Salesman Problem" max cut location problems network design flows and paths quadratic and 3-dimensional assignments linear assignment vehicle routing cutting and packing combinatorial topics in VLSI design applications in computational biology.