An algebraic approach to group schemes actions

The aim of this Oberseminar is to present an algebraic way of studying (finite) group schemes actions, which has been fruitful for a complete study of the actions of a specific class of group schemes.
In order to do this, we will start with some recallings on group schemes, pointing out differences occurring in characteristic zero and positive. We will then move on to their actions and explain how to construct them in an algebraic way.
The objective is to present the subject in a concrete and accessible way: with this in mind, the presentation will be guided by various examples.