Elastic plates form a class of very important mechanical structures that occur in a wide range of practical applications, from building to microchip production. In this Monograph, the authors explore a number of important problems encountered in working with elastic plates. This is the first book to consider so many fundamental boundary value problems in conjunction with both variational and potential methods for finite and infinite domains. The authors write very explicitly, with full explanations, and conduct the discussion in Sobolev spaces to yield useful results for error analysis in numerical computations.