There are optimization problems where all variables are integer. The introduction of this chapter shows that naïve solution approaches can be misleading. In consequence, specific strategies must be devised, like cutting plane techniques or branch and bound methodology. The chapter introduces these strategies, including examples and programs in MATLAB. Then, important application examples are treated: facility location, capital budgeting, the travelling salesman problem (TSP), the cutting stock problem (and column generation). The chapter ends with three more topics: algorithmic cuts, unimodular matrices, and mixed-integer linear programming (some variables are integer, others not).