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 and abelian varieties, each with unique properties and applications. These groups help mathematicians understand symmetries and transformations in a structured way.