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.