This book is intended to serve as a unique and comprehensive textbook for scientists and engineers as well as advanced students in thermo-fluid courses. It provides an intensive monograph essential for understanding dynamics of ideal fluid, Newtonian fluid, non-Newtonian fluid and magnetic fluid. These distinct, yet intertwined subjects are addressed in an integrated manner. It starts with coherent treatment of fundamental continuum mechanics, with an emphasis on the intrinsic angular momentum, by which the concepts of ferrohydrodynamics are progressively built up, and serve as a foundation for later development. Flows of ideal and Newtonian fluids are followed by a detailed presentation of basic continuum equations for applications of fluid engineering, which cover the design and operations of various turbomachines, heat exchangers and flow elements. The study of the deformation and flow of matter, namely rheology, is discussed primarily with regard to the stresses generated during the flow of complex materials, which are represented by viscoelastic fluids. Throughout the book, the first priority is to illustrate the utilization of constitutive equations (relations) in order to facilitate an understanding of the physical flow phenomena and mechanisms. Moreover, it enables readers to classify flows and specific engineering problems, which can then be identified and formulated. In order to make the book self-contained, many exercises and problems are provided for each chapter in addition to the numerous pedagogical aids that have been incorporated throughout. The intention is to facilitate the reader to compose their knowledge into a better understanding of both the theoretical and applicable aspects of fluid engineering.