
## 79.1 Introduction

Formal schemes were introduced in [EGA]. A more general version of formal schemes was introduced in and another in [Yasuda]. Formal algebraic spaces were introduced in [Kn]. Related material and much besides can be found in [Abbes] and . This chapter introduces the notion of formal algebraic spaces we will work with. Our definition is general enough to allow most classes of formal schemes/spaces in the literature as full subcategories.

Although we do discuss the comparison of some of these alternative theories with ours, we do not always give full details when it is not necessary for the logical development of the theory.

Besides introducing formal algebraic spaces, we also prove a few very basic properties and we discuss a few types of morphisms.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).