Algebra arises from the study of equations and polynomials. From this there has arisen a rich selection of modern algebraic structures, such as, groups, fields, rings and Lie-algebras.

Algebra becomes particularly interesting when it interacts with other mathematical fields, such as, combinatorics, topology, geometry or physics.

In algebraic geometry, one studies geometric objects that naturally have algebraic structure: curves, surfaces and higher-dimensional spaces that can be defined by polynomial equations. Here, there is a rich interaction with modern algebra, topology and complex analysis. Some of the problems are classical and go back for up to two hundred years, while others are related to problems in physics and coding theory.