Oort: LNM0015 studies some aspects of group schemes.
Various things in the Alg gps and gp schemes folder under AG.
Kevin’s course on group schemes, autumn 2006: My informal course title contains the word “scheme” but you don’t have to know what a scheme is to follow the course because I will be sticking to the affine case (in other words, you only have to know what a commutative ring is, and basic notions up to tensor products of modules; see e.g. Atiyah–Macdonald). I’ll start by introducing the notion of a commutative affine group scheme, which is just a ring equipped with some extra structure, and will do lots of examples. Then I’ll develop some of the theory from the ground up: I’ll define the module of differentials and prove basic results bout it, and I’ll classify finite group schemes over a perfect field. At this stage I’ll either prove the necessary results from commutative algebra myself, or give precise references.
After this introductory beginning, I will then go on to the case where the base is the integers of a finite extension of Q_p and explain some subset of the following: results of Oort-Tate and Raynaud (about group schemes killed by p), results of Tate and Fontaine (about discriminants of the rings that can show up here), results of Fontaine and others about p-divisible groups when the base is not too ramified, and finally results of Breuil and others when the base is highly ramified. The course will be in the “accelerated lecture style” in the sense that at the beginning I’ll assume very little and give full proofs, and then as the term goes on and I begin to panic I’ll start assuming more and more of the audience.
nLab page on Group scheme