This book is a monograph devoted to the rigorous analysis of several of the most important stationary boundary value problems that appear in Fluid Mechanics. We study mainly the Stokes, Navier-Stokes, Oseen, Brinkman, and Darcy-Forchheimer-Brinkman systems. These systems are formulated in bounded and exterior Lipschitz domains in \(\mathbb R^{n}\) or in domains with cylindrical ends. For their study, we use mainly integral operators methods. These methods are complemented with variational methods. The results presented in this monograph are at the forefront of the research in the field and are due mainly to its authors, but results due to other researchers are also included. Nevertheless, we tried to make them accessible to graduate students and to a wide range of researchers interested in Partial Differential Equations or in Fluid Mechanics, not just to specialists in the field. To this end, we have included a significant amount of background material, complete proofs of our results, and a detailed appendix that provides an introduction to auxiliary topics needed for understanding this monograph. This monograph is divided into four parts.