The Monster Group and Its 196884-Dimensional Space

The Monster simple group was first constructed by R.L. Griess in 1981 as the group of automorphisms of a certain algebra in Euclidean space of dimension 196884. This chapter describes the simplified construction given in [Con15]. The construction is based on the binary Golay code, the Leech lattice, and a remarkable nonassociative loop (closely related to the Golay code) discovered by R.A. Parker.