In the course Set theory and algebra (2WF40) you came across calculations with integers and polynomials . These calculations were carried out in an algebraic structure, a set with a number of algebraic operations,such as the integers or a polynomial ring. 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 computational and algorithmic aspects. The abstract approach helps for instance in recognizing common aspects in various concrete settings. Such structures are used in a variety of branches of science like mathematics (e.g., coding theory, cryptography, symmetry, differential geometry), physics (e.g., string theory), chemistry (e.g., crystallography) and belong to the core of mathematics. The course 2WF70 Algorithmic Algebra and Number Theory is a sequel to this course. The elective course 2WF80 Introduction to Cryptology uses various concepts discussed in 2WF50. In the master Industrial and Applied Mathematics, various courses make use of 2WF50. Historical aspects are discussed in the elective course 2WH60 Mathematics and Practice in Historical Perspective.