This book began as lecture notes for an Oregon State University course in fluid mechanics, designed for beginning graduate students in physical oceanography. Because of its fundamental nature, this course is often taken by students outside physical oceanography, e.g., atmospheric science, civil engineering, physics and mathematics. In later courses, the student will discover esoteric fluid phenomena such as internal waves that propagate through the sky, water phase changes that govern clouds, and planetary rotation effects that control large-scale winds and ocean currents. In contrast, this course concerns phenomena that we have all been familiar with since childhood: flows you see in sinks and bathtubs, in rivers, and at the beach. In this context, we develop the mathematical techniques and scientific reasoning skills needed for higher-level courses and professional research.