  In this thesis, topologically massive Yang-Mills theory is studied in the
framework of geometric quantization. This theory has a mass gap that is
proportional to the topological mass $m$. Thus, Yang-Mills contribution decays
exponentially at very large distances compared to $1/m$, leaving a pure
Chern-Simons theory with level number $k$. The focus of this research is the
$near$ Chern-Simons limit of the theory, where the distance is large enough to
give an almost topological theory, with a small contribution from the
Yang-Mills term. It is shown that this almost topological theory consists of
two copies of Chern-Simons with level number $k/2$, very similar to the
Chern-Simons splitting of topologically massive AdS gravity model. As $m$
approaches to infinity, the split parts add up to give the original
Chern-Simons term with level $k$. Also, gauge invariance of the split
Chern-Simons theories is discussed for odd values of $k$. Furthermore, a
relation between the observables of topologically massive Yang-Mills theory and
Chern-Simons theory is obtained. It is shown that one of the two split
Chern-Simons pieces is associated with Wilson loops while the other with 't
Hooft loops. This allows one to use skein relations to calculate topologically
massive Yang-Mills theory observables in the near Chern-Simons limit. Finally,
motivated with the topologically massive AdS gravity model, Chern-Simons
splitting concept is extended to pure Yang-Mills theory at large distances. It
is shown that pure Yang-Mills theory acts like two Chern-Simons theories with
level numbers $k/2$ and $-k/2$ at large scales. At very large scales, these two
terms cancel to make the theory trivial, as required by the existence of a mass
gap.
