Pt. 1. Fourier Series and Periodic Distributions -- 1. Preliminaries -- 2. Fourier Series: Basic Theory -- 3. Periodic Distributions and Sobolev Spaces -- Pt. 2. Applications to Partial Differential Equations -- 4. Linear Equations -- 5. Nonlinear Evolution Equations -- 6. The Korteweg-de Vries Equation -- Pt. 3. Some Nonperiodic Problems -- 7. Distributions, Fourier Transform and Linear Equations -- 8. KdV, BO and Friends -- App. A. Tools from the Theory of ODEs -- App. B. Commutator Estimates