Applications of frames in different sciences encouraged the author to present some extensions of frames in both Hilbert and Banach spaces. Some years ago, Ole Christensen published two great books on frame theory. His books provide the fundamental theorems and properties of frames in Hilbert spaces. The main aim of this book is to provide the new applications of frames, have been motivating the existence of some extensions and generalizations of frames. During the past few years, frames have become increasingly popular and several explicate contractions and applications motivated the researchers for introducing some new concepts that originally coming from frame theory, like continuous frames, fusion frames, g-frames, continuous g-frames and etc.