Beginning with this chapter and throughout this second part of the book, we will consider anisotropic, variable coefficient systems. For these systems, a fundamental solution is usually not known. This requires us then to use variational techniques to first prove the existence and uniqueness of the solution for the problem formulated in the entire space (so without boundary conditions). Once this is achieved, the layer potentials are defined by using the existence and uniqueness result for suitable data. More specifically, in this chapter, we study a Stokes system with a strongly elliptic viscosity coefficient tensor and its layer potentials. In turn, this allows us to study transmission problems for the anisotropic Stokes and Navier-Stokes systems in \(L^p\) -based weighted Sobolev spaces on \(\mathbb R^{n}\) ( \(n = 3\) or \(n = 4\) for the Navier-Stokes system).