This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Leray problem on existence of a solution to the boundary value problem for the stationary Navier—Stokes system in bounded domains under sole condition of zero total flux. This marks the culmination of the authors work over the past few years on this under-explored topic within the study of the Navier—Stokes equations. This book will be the first major work on the Navier—Stokes equations to explore Leray problem in detail. The results are presented with detailed proofs, as are the history of the problem and the previous approaches to finding a solution to it. In addition, for the reader convenience and for the self-sufficiency of the text, the foundations of the mathematical theory for incompressible fluid flows described by the steady state Stokes and Navier—Stokes systems are presented. For researchers in this active area, this book will be a valuable resource.