The goal of  this lecture is to provide the students with an account of the most recent algebraic techniques used to classify the complexity of cmputational problems called Constraint Satisfaction Problems. Students will be prepared to conduct further research in the area at any level (master, PhD or postdoc).

After a short introduction to the basics of complexity  theory (Turing machines, the class NP), we consider computational problems naturally related with first-order structures. We then focus on certain such problems called Constraint Satisfaction Problems (CSPs). We develop algebraic tools which are useful in the classification of the complexity of CSPs.