The area of wave structure interaction is a major branch of fluid mechanics and assumes special significance due to its wide range of application in Marine Technology and Arctic Engineering. The objective of the proposed monograph is to present a contemporary account of various mathematical techniques on wave structure interaction problems and to deal with a class of initial/boundary value problems associated with Laplace equation satisfying certain higher order boundary conditions. These classes of boundary value problems are not of the Sturm-Liouvillc type in nature and arc rarely discussed in any text books. All efforts arc made to present the material in the monograph in a pedagogical manner to enable the readers to appreciate various tools discussed and apply them to their own problems in related branches. At the end of each chapter, certain exercises are left for the readers; some of these exercises are not yet attempted for solution. The content is divided into seven chapters based on the application of the various mathematical techniques and the discussed physical problems.