This document discusses useful Java methods including accessors and mutators, the toString() method, test classes, and the equals() method. It explains that accessors and mutators allow external classes to access or modify private member variables, and that toString() creates a string representation of an object. It demonstrates how to test classes and override equals() to define object equality. The document advises using instanceof when overriding equals() for safety and recommends leveraging IDE features to generate common methods.