Imparts a self–contained development of the algebraic theory of Kac–Moody algebras, their representations and close relatives—-the Virasoro and Heisenberg algebras. Focuses on developing the theory of triangular decompositions and part of the Kac–Moody theory not specific to the affine case. Also covers lattices, and finite root systems, infinite–dimensional theory, Weyl groups and conjugacy theorems.