In this thesis we are concerned with the study of covariant transform which generalizes the idea of wavelets transform on Hilbert and Banach spaces. The properties of covariant transform on Locally convex spaces like continuity and boundedness are studied. We illustrate the general theory by consideration the ax+b group in details. This example has a close relation to various techniques in harmonic analysis. Moreover, some properties of the image space W_FV is discussed. The properties of the contravariant transform on locally convex spaces are investigated as well. Also, various examples of covariant and contravariant transforms are introduced.