Abstract: In this session I will talk about rationality of algebraic tori. We will first define the notion of rational algebraic variety and then some relaxed notions of rationality. Algebraic tori are important objects in studying algebraic groups.

The rationality problem for an arbitrary group is difficult. Hence it makes sense to study the problem for algebraic groups which have a simple structure.

In order to talk about rationality of algebraic tori we will take a look at the duality between the category of split algebraic tori and the category of G-lattices. We will end the session with the main results about birational classification of tori in small dimensions.