  We develop an ab initio analytic theory of random lasing in an ensemble of
atoms that both scatter and amplify light. The theory applies all the way from
low to high density of atoms. The properties of the random laser are controlled
by an Euclidean matrix with elements equal to the Green's function of the
Helmholtz equation between pairs of atoms in the system. Lasing threshold and
the intensity of laser emission are calculated in the semiclassical
approximation. The results are compared to the outcome of the diffusion theory
of random lasing.
