We consider M theory 5-branes with compact transverse dimensions. In certain limits the theory on the 5-brane decouples and defines " little string theories " in 5 + 1 dimensions. respectively has a perfect parallel in a theory of strings and membranes in 6, 7, 8 dimensions. We call these theories a/b, m, f theories. They have a coupling constant but no gravity. This construction clarifies some mysteries in F-theory and leads to several speculations about the phase structure of M theory.