In Geometric Invariant Theory, by Mumford, Fogarty, and Kirwan, if there is a mention of descent theory, it almost always comes along with a reference to SGA 8, Theorem 5.2 (see the end of the proof of prop 6.9 on page 119, for example). Now I know SGA 8 was never made, but I was wondering:


1. Does anyone have a good guess as to what this theorem should say?
2. Does anyone have a good reference for a quick and "hands off" introduction to descent theory? I am really just looking to understand the "gist" of it.



References to SGA 8 and descent theory
For question 1, see the comment above.


Collecting the answers to question 2:


* Grothendieck's original *FGA*, starting with [TDTE I](http://www.numdam.org/numdam-bin/fitem?id=SB_1958-1960__5__299_0)
* Vistoli's chapter in *FGA explained*, for the connection with stacks
* [What is descent theory?](https://mathoverflow.net/questions/22032/what-is-descent-theory) for a very short overview
* Bosch-Lütkebohmert-Raynaud, *Néron Models* (recommended by BCnrd in the above-mentioned thread)
* Waterhouse, *Introduction to Affine Group Schemes*, containing a 20-page introduction primarily concerned with the affine case


"Community wiki" post, feel free to modify.


