An algebraic group is a mathematical structure that combines concepts from both algebra and geometry. It consists of a set of elements that can be combined using a group operation, while also being defined by polynomial equations. This means that the group can be studied using the tools of algebraic geometry, which focuses on the solutions of these equations. Algebraic groups are important in various areas of mathematics, including number theory and representation theory. They can be classified into different types, such as linear algebraic groups, which are represented by matrices, and abelian varieties, which are more complex structures related to elliptic curves and complex tori.