The goal of the first lecture is to describe extended affine root systems (EARS), a generalization of finite and affine root systems. This is most naturally done in the context of affine reflection systems. I will also discuss the structure of the associated Weyl groups, i.e., the groups generated by all reflections.

The second lecture will be devoted to Lie algebras, in which EARS naturally occur as roots of a Cartan subalgebra, the so-called extended affine Lie algebras (EALAs). I will discuss the structure of EALAs, in particular their description in terms of Lie tori.

The talks do not assume any prior knowledge of EARS or EALAs, but some understanding of finite root systems and of finite-dimensional simple Lie algebras will be necessary.