Drawing on the author's lectures on fluid mechanics modeling, this text takes a rigorous approach to the topic while maintaining a clear, easy-to-understand style. It deals with the main physical phenomena that occur in slow, inertialess viscous flows commonly encountered in various industrial, biophysical, and natural processes. Suitable for students in chemical or mechanical engineering, bioengineering, and physics, the book discusses a wide variety of topics, including confined flows, complex fluids, and rheology. Each situation is illustrated with examples and multi-part problems that stress analytical solutions and the physical interpretation of the mathematical results.