  In this paper we present Affine.m - program for computations in
representation theory of finite-dimensional and affine Lie algebras and
describe implemented algorithms. Algorithms are based upon the properties of
weights and Weyl symmetry. The most important problems for us are the ones,
concerning computation of weight multiplicities in irreducible and Verma
modules, branching of representations and tensor product decomposition. These
problems have numerous applications in physics and we provide some examples of
these applications. The program is implemented in popular computer algebra
system Mathematica and works with finite-dimensional and affine Lie algebras.
