This book presents a contemporary account of research on various mathematical/numerical techniques to deal with the interaction of surface gravity waves with flexible floating/submerged structures which are available in the scientific literature in a scattered manner. It emphasizes unique determination of the solution for a class of physical problems associated with Laplace or Helmholtz type equations, applications of the theory of ordinary and partial differential equations, Fourier Analyses etc. It provides a toolkit to a large section of the scientific community including mathematicians, physicists and engineers working on fluid structure interactions.