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### 1. Introduction

#### 1.1 Philosophy

Forms is a package for computation with sesquilinear and quadratic forms on finite vector spaces. It provides users with the basic tools to work with classical groups and polar geometry, and enables one to specify a form and its corresponding geometry. Also included in the functionality of the package are operations which allow a user to change coordinates; or to ``change form'' and work in an isometric (or similar) polar space.

#### 1.2 Overview over this manual

The next chapter (2.) gives some basic examples of the use of this package. In "Background Theory of Forms" (Chapter 3.) we revise the basic notions of the theory of sesquilinear and quadratic forms, where we also set the notation and conventions adopted by the this package. In Sections 4.1, 4.2, and 4.3 we provide the details of the operations, functions, and attributes entailed in Forms.

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