  This is my PhD thesis. In this thesis we study the gauge theories on
noncommutative Moyal space. We find new static solitons and instantons in terms
of the so called generalized Bose operators. Generalized Bose operators are
constructed to describe reducible representation of the oscillator algebra.
They create/annihilate $k$-quanta, $k$ being a positive integer. We start with
giving an alternative description to the already found static magnetic flux
tube solutions of the noncommutative gauge theories in terms of generalized
Bose operators. The Nielsen-Olesen vortex solutions found in terms of these
operators reduce to the already found ones. On the contrary we find a class of
new instaton solutions which are unitarily inequivalant to the the ones found
from ADHM construction on noncommutative space. The charge of the instaton has
a description in terms of the index representing the reducibility of the Fock
space, i.e., $k$. After studying the static solitonic solutions in
noncommutative Minkowski space and the instaton solutions in noncommutative
Euclidean space we go on to study the implications of the time-space
noncommutativity in Minkowski space. To understand it properly we study the
time-dependent transitions of a forced harmonic oscillator in noncommutative
1+1 dimensional spacetime. We also try to understand the implications of the
found results in the context of quantum optics. We then shift to the so called
DSR theories which are related to a different kind of noncommutative
($\kappa$-Minkowski) space. DSR (Doubly/Deformed Special Relativity) aims to
search for an alternate relativistic theory which keeps a length/energy scale
(the Planck scale) and a velocity scale (the speed of light scale) invariant.
We study thermodynamics of an ideal gas in such a scenario.
