In mathematics, E8 is the name given to an exceptional simple Lie group of dimension 248 (see below); the same notation is sometimes used for its root lattice, which has rank 8. The group E8 was discovered between the years of 1888 and 1890 by Wilhelm Killing, though he did not prove its existence, which was first shown by Élie Cartan.

The designation E8 comes from Killing and Cartan's classification of the complex simple Lie algebras, which fall into four infinite families labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E8 algebra is the largest and most complicated of these exceptional cases, and is often the last case of various theorems to be proved.