- Ordinary Differential Equations. First-Order Ordinary Differential Equations
- Higher Order Ordinary Differential Equations
- Special Functions
- Partial Differential Equations. First-Order or Linear Equations
- Nonlinear Scalar Equations
- Nonlinear Schrödinger and Davey-Stewartson Equations
- Dynamic Convection in a Sea
- Boussinesq Equations in Geophysics
- Navier-Stokes Equations
- Classical Boundary Layer Problems.

This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrödinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer problems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations, linearization techniques and special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering.