This course is intended to be a first graduate-level course in fluid mechanics, and assumes that students have had at least one introductory fluid mechanics course at the undergraduate level. The course starts with a review of vectors, tensors, and related theorems; flow kinematics; derivations of the differential forms of the governing equations of fluid motion. Then the following subjects are covered: exact solutions (solutions with parallel boundaries, solutions with circular symmetry, pulsating flows, stagnation-point flows, etc.); special forms of governing equations (Kelvin's theorem, vorticity transport theorem, equations for inviscid flow (Euler); and boundary layer theory (boundary layer equations, boundary layer on a flat plate: Blasius solution, approximate solutions, effect of pressure gradient, separation, perturbation techniques, stability of boundary layers, etc.)