Textbook in PDF format Theoretical and Computational Fluid Mechanics: Existence, Blowup and Discrete Exterior Calculus Problems, Volume II is self-contained, though it builds upon the work of the previous volume in providing a comprehensive introduction to the mathematical theory of incompressible flows, with a focus on the foundational structures, analytical techniques, and open problems associated with the Navier-Stokes equations. In this volume, emphasis is placed on the interplay between geometry, functional analysis, and partial differential equations that underpins much of modern fluid theory. As a reference or teaching supplement, the book is accessible to anyone with a basic level of understanding of fluid dynamics and yet still engaging for those of a deeper understanding. The book is aimed at theorists and applied mathematicians from a wide range of scientific fields, including the social, health, and physical sciences. It provides a step-by-step guide to the construction of solutions of both elementary and open problems of viscous and non-viscous models, and for the applications of such models for the functional analysis and real analysis of data