For a long time, Combinatorics was considered mainly as recreational mathematics. But in the past few decades, it has emerged as a mainstream area, with rich connections with more classical ones such as algebra, topology, geometry and probability theory. Moreover, because of its close links with computer science, Combinatorics has become a crucial scientific endeavor.
Besides classical tools, like the pigeonhole principle, the inclusion-exclusion principle, the double counting argument, induction, Ramsey argument, etc., some recent tools (the probabilistic, the algebraic, the linear algebra, the analytical and the topological methods) have shown their surprising power in solving a lot of combinatorial problems (classical and new ones). For example, with a mere knowledge of the concepts of linear independence and discrete probability, beautiful connections can be made between algebra, probability, and combinatorics. These new techniques have also found striking applications in other areas of discrete mathematics and the theory of computing.
Despite the beauty, the breadth and depth of results and applications of Combinatorics, research and teaching in this field are underrepresented in Argentina and South America. One of the main purposes of this school is to change this situation, by bringing a "guided tour" covering its most important branches, and by demonstrating its methods and power. Another related objective is the creation of research and academic networks and to build a frame for the interchange of ideas in this field.