Reductive groups are a class of algebraic groups that can be understood through their representation theory. They are characterized by the property that every representation can be decomposed into a direct sum of irreducible representations. This means that the structure of these groups is relatively simple and well-behaved, making them easier to study in various mathematical contexts. These groups play a significant role in many areas of mathematics, including algebraic geometry, number theory, and theory of Lie groups. Examples of reductive groups include GL(n), the group of invertible n x n matrices, and SL(n), the group of n x n matrices with determinant one.