The 1998 Type Ia Supernova observation revealed a extremely surprising and confusing conclusion on Cosmology. As a result the 2011 Nobel Prize in Physics have been awarded to Saul Perlmutter, Brian Schmidt and Adam Reiss on the discovery of Accelerating Universe. The mysterious candidate responsible for such condition of the Universe is refered to as "Dark Energy". Some recent observations on supernovae velocities suggests the universe may be expanding non-uniformly in its acceleration. In this book the Universe is considered as "Anisotropic Universe" and how the different Dark Energy models can dominate it to speed up the expansion has been explained thoroughly with the support of some geometrical parameters and 2D, 3D figures.