"An Introduction to the Mathematical Theory of the Navier-Stokes Equations" offers a comprehensive and detailed treatment of the fundamental mathematical properties of boundary value problems associated with the Navier-Stokes equations. The book addresses central topics such as the existence, uniqueness, and regularity of solutions in both bounded and unbounded domains. For unbounded domains, the asymptotic behavior of the solutions is also examined. This new edition combines the original two volumes into one and includes additional chapters on stationary generalized Oseen flows in exterior domains as well as stationary Navier-Stokes flows in three-dimensional exterior domains. The introductory first chapter outlines relevant questions and motivates significant, still open issues. Each chapter is accompanied by an extensive discussion of the problems addressed and concludes with alternative approaches and historical notes. Over 400 stimulating exercises of varying difficulty levels support students and early-career researchers in becoming familiar with the topic.