This chapter outlines some basic techniques and results on layer potentials for the isotropic, constant coefficient Stokes and Brinkman systems on bounded or on exterior Lipschitz domains. The layer potentials are introduced and studied by taking advantage of the availability of explicit formulas for the fundamental solutions. In particular, we prove mapping and invertibility properties of some potential theory integral operators for the Stokes and Brinkman systems. This allows us to establish the well-posedness of the Dirichlet and Neumann problems for the Brinkman system in \(L^p\) -based Besov spaces in bounded Lipschitz domains in \(\mathbb R^n\) , \(n\geq 3\) . Using Fredholm operators techniques, we extend the well-posedness result to the mixed problem for the Brinkman system in \(L^p\) -based spaces in bounded Lipschitz creased domains. This chapter is a good illustration of the classical approach to layer potentials.