One of the most important problems of modern society is the processing of vast amounts of data to make the best decision. One of the promises of the information technology era is that many decisions can now be made rapidly by computers. The science of how to make decisions in order to achieve some best possible goal has created the field of combinatorial or discrete optimization.     Combinatorial optimization is one of the most active areas of discrete mathematics. It has been the subject of extensive research for over fifty years. Combinatorial optimization has its roots in combinatorics, theoretical computer science and operations research. A main motivation is that hundreds or thousands of real-life problems and phenomena can be considered as combinatorial optimization problems. Therefore, the design of combinatorial algorithms now is a vast area containing many strong techniques for various applied problems.  The course `Combinatorial Optimization’ includes the fundamentals of graph theory, linear and integer programming, and complexity theory. The course covers classical topics in combinatorial optimization as well as very recent results. It consists of two big parts. Most of the problems considered in the first part have efficient algorithms. Optimal solutions of these problems can be found in time polynomial in the size of the input. While most of the problems studied in the second part of the course are NP-hard. A polynomial-time algorithm for NP-hard problems is unlikely to exist. However, in many cases one can at least find approximation algorithms with provably good performance.