This book presents a comprehensive and rigorous introduction to the fundamental principles and differential equations that govern the kinematics and dynamics of laminar flow of incompressible Newtonian fluids. Furthermore, it simultaneously illustrates the application of numerical methods to computing a variety of flow variables and solving a broad range of problems, and discusses the development of specific computational algorithms. The numerical procedures are developed from first principles, no experience in Computational Fluid Dynamics and knowledge of terminology is required, and references for specialized topics are provided. The material is intended to be instructive in the classroom and useful as a source reference to advanced undergraduate students, graduate students and researchers in the various fields of engineering, including chemical, mechanical and aerospace engineering, applied mathematics, and computational science. Topics include the computation of stationary interfacial shapes, the derivation of exact solutions to the equation of solving ordinary differential equations, hydrodynamic stability, flow at low Reynolds numer, vortex motion, boundary integral methods for potential and creeping flow, and finite-difference methods.