Universal algebra is a branch of pure mathematics which studies equationally defined classes of arbitrary algebraic structures. In the 1990s, Jeavons began championing the use of universal algebra to classify tractable constraint satisfaction problems; the methodology he introduced has found increasingly significant application, particularly in attacking the Dichotomy Conjecture of Feder and Vardi.

The first two lectures of this tutorial will give an introduction to the jargon and tools of universal algebra which are most relevant to CSP. After a quick introduction to the basic objects and constructions, I will review the classical correspondence between finite algebras and finite relational structures and then explore the phenomenon of Maltsev conditions (equations satisfied by polymorphisms) restricting the complexity of relational structures. Some fundamental algebraic dichotomies, first discovered using tame congruence theory, will be presented in the important idempotent case.

In the latter two lectures I will sample some of the achievements of the algebraic methodology in CSP. Topics will include the algebraic dichotomy conjecture, the delineation of templates with bounded width, the few subpowers algorithm, and the fine-structure dichotomy conjectures. Throughout, I hope to illustrate arguments that are typical from an algebraic (or at least functional) point of view.