  The present thesis represents developments in two main directions related to
the simple Lie algebras. The first one is devoted to the representation theory
of the simple Lie algebras. Specifically, we present recent results, which
include new universal formulae in Vogel's universal description, as well as the
discovery of additional properties of those formulae. In the second part of the
thesis, we demonstrate applications of Vogel's description to the study of a
physical theory. Namely, we explicitly formulate the { \it refined}
Chern-Simons theories on $S^3$ for each of the simple gauge groups, including
the exceptional ones.
