0. The Foundations: A Brief Introduction 1. An Introduction to Partial Differential Equations 2. Partial Differential Equations of Second Order 3. Elliptic Differential Equations 4. Parabolic Differential Equations 5. Hyperbolic Differential Equations 6. Green, Dirac Delta and Harmonic Function 7. Canonical Form and Riemanns Method 8. THe Laplace Transform and Its Application to Partial Differential Equations 9. Fourier Transforms and Its Application to Partial Differential Equation 10. Calculus of Variations 11. Additional Topics 12. Representations of Solutions 13. Numerical Solution of Partial Differential Equations