The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations,　as well as　numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations.

Included for nearly every method are:

The types of equations to which the method is applicable

The idea behind the method

The procedure for carrying out the method

At least one simple example of the method

Any cautions that should be exercised

Notes for more advanced users

The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.