The constraint satisfaction problem (CSP) provides a general framework in which it is possible to express many problems encountered in mathematics, computer science, and artificial intelligence.

In this course we will introduce the CSP framework, in several equivalent mathematical formulations (including systems of constraints, logical formulas, and homomorphisms between graphs and relational structures), and demonstrate how a wide range of well-known problems can be naturally expressed in it. We will then exhibit a variety of CSP-related mathematical and computational questions that have been studied in the last decade, and explain their relevance. Finally, we will overview the mathematical techniques (other than those presented in depth in three other courses within the summer school) used to tackle these questions, and present a list of open problems.