Abstract

" p-adic fields provide remarkable, easy and natural solutions to problems which apparently have no relation to p-adic fields and which otherwise can be resolved, if at all, only by deep and arduous methods ". -- J. W. S. Cassels The first Local-Global Principle, formulated by Hasse in 1921, relates the behaviour of rational quadratic forms in [Special characters omitted.] (global field) to their behaviour in the p -adic fields [Special characters omitted.] (local fields). The notion of using local information as a stepping stone towards understanding more difficult global properties has been generalized and applied to many problems, making Local-Global methods a powerful number theoretic tool. Even when the principle fails, we can sometimes salvage some connection between the local and the global. This thesis aims to give a survey of the basic theory.