The theme of this chapter is the correspondence between algebraic groups and Lie algebras, which we call the Lie correspondence. This correspondence works very well in characteristic 0, but is notably less powerful in positive characteristic. For this reason all base fields in this chapter will be assumed to be of characteristic 0 (unless otherwise stated). As in the previous chapters, K denotes an algebraically closed field, whereas k, k ’, . . . denote not necessarily algebraically closed fields.