Linear algebraic groups are a class of mathematical structures that combine concepts from algebra and geometry. This suggests that algebraic groups can be approached from different perspectives, such as Group Theory, Algebraic Geometry, and Combinatorics. They have applications in several directions (Invariant Theory, Physics). Linear algebraic groups are affine varieties with a compatible group structure. They were introduced in the late 1800s to study continuous symmetries of differential equations. An important class of algebraic groups consists of non connected algebraic groups. 

In the first part of the talk I will introduce basic notions and examples of linear algebraic groups, and in particular of non connected linear algebraic groups. 

The last part of the presentation is devoted to explore some partition of these objects, in particular Jordan classes and Lusztig strata, and investigating their geometric properties.