  We lay down the preliminary work to apply the Functional Analytic Approach to
quasi-periodic boundary value problems for the Helmholtz equation. This
consists in introducing a quasi-periodic fundamental solution and the related
layer potentials, showing how they are used to construct the solutions of
quasi-periodic boundary value problems, and how they behave when we perform a
singular perturbation of the domain. To show an application, we study a
nonlinear quasi-periodic Robin problem in a domain with a set of holes that
shrink to points.
