ABSTRACT
This chapter presents an introduction to algebraic groups. It aims to define algebraic groups, and describes some basic properties and constructions regarding algebraic groups. Among these, one of the most prominent certainly is the construction of the Lie algebra of an algebraic group. This will play an important role throughout the book, for the theory as well as for the algorithms. The chapter discusses some basic algorithmic problems for algebraic groups, among which is the construction of the Lie algebra. It focuses on ways to specify an algebraic group suitable for computation. The chapter also describes how the unipotent radical of an algebraic group is defined. When computing with algebraic objects one must decide how the input and output of the algorithms are defined, that is, how the various objects are represented by a finite amount of data.
