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This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Leray's 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's 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's 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.