CONTENTS :- 1. INTRODUCTION, 2. FIRST ORDER PARTIAL DIFFERENTIAL EQUATION, 3. CLASSIFICATION OF SECOND ORDER LINEAR PDE AS HYPERBOLIC PARABOLIC OR ELLPTIC, 4. REDUCTION OF SECOND ORDER LINEAR EQUATIONS TO CANONICAL FORMS, 5. INTRODUCTIONS OF HEAT, WAVE AND LAPLACE EQUATIONS, 6. NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF FIRST ORDER : STANDARD FORMS, 7. CHARPITS METHOD, 8. HIGHER ORDER LINEAR PARTIAL DIFFERENTIAL, 9. MONGES METHOD, 10. SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS, 11. A LINEAR SYSTEM IN NORMAL FORM, 12. MATRIX METHOD FOR HOMOGENEOUS LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS,