  We provide a rigorous mathematical foundation to the study of strongly
rational, holomorphic vertex operator algebras V of central charge c = 8, 16
and 24 initiated by Schellekens. If c = 8 or 16 we show that V is isomorphic to
a lattice theory corresponding to a rank c even, self-dual lattice. If c = 24
we prove, among other things, that either V is isomorphic to a lattice theory
corresponding to a Niemeier lattice or the Leech lattice, or else the Lie
algebra on the weight one subspace V_1 is semisimple (possibly 0) of Lie rank
less than 24.
