In this thesis, we develop the theory of frames in Hilbert modules over locally - algebras and present many theorems of frames in Hilbert modules over locally - algebra instead of Hilbert spaces. Frames were introduced by Duffin and Schaffer in their fundamental paper. They used frames as a tool in the study of nonharmonic fourier series. Daubechies, Grossmann and Meyer observed that the frames can be used to find series expansions of functions in (R) that are very similar to the expansions using orthonormal basis. A frame is a sequence of element in H, whitch allows every f to be written as an countable linear combinations of element in the frame. However, the corrospounding coefficient are not necessarily unique.