This course is intended as an introduction to the homology and cohomology theory of algebras, concentrating on the construction and properties of Hochschild homology, cyclic homology and its variants. These (co)homology theories have important applications in many areas, e.g. in commutative algebra, non-commutative algebra, algebraic K-theory and (in global versions) algebraic geometry and mathematical physics. There are also generalizations using stable homotopy theory methods that allow us to study products structures up to infinite homotopy and the associated deformation theory.

The course will be accessible to anyone with a basic knowledge of algebra and homological algebra.