We survey the structure theory of connected reductive groups over an algebraically closed field. We explain how reductive groups, such as linear groups, orthogonal groups and symplectic groups, are "combinatorial," i.e. controlled by root data. We also explain the relation to several closely related categories, such as that of connected compact Lie groups and that of semisimple complex Lie algebras. We will put our emphasis on examples, while the proofs will mostly be omitted or merely sketched. We also plan to talk about the theory of highest weight representations.

We assume the audience are familiar with algebraic varieties. Familiarity with algebraic tori will also help.