In the course Set theory and algebra (2WF40) you came across calculations with integers, polynomials and permutations. These calculations were carried out in an algebraic structure, a set with a number of algebraic operations. In the present course we focus on an abstract set-up of such algebraic structures and concentrate mainly on so-called groups, rings, fields and some algorithmic aspects. Such structures are used in a variety of branches of science like mathematics (e.g., cryptography), physics (e.g., string theory), chemistry (e.g., crystallography) and belong to the core of mathematics. The course 2WF70 is a sequel to this course.