Locally compactness in topological groups

In this study, topological groups, right(left) topological groups, paratopological groups and quasi-topological groups were examined and relevant examples were given. Some properties of topological groups are discussed by making use of the fact that right(left) topological groups are homogeneous spaces and right(left) translational transformations are homeomorphism. Some features of the quotients of topological groups were observed. In case G is a topological group and H is a locally compact subgroup of G, the properties provided by G/H are examined.