Wonderful varieties with a view towards Poisson geometry

These are expanded lecture notes from the author’s minicourse at the 2022 Poisson Geometry Summer School, which took place at the Centre de Recerca Matematica in Barcelona, Spain. After giving a general introduction to wonderful varieties, and an explicit construction of the wonderful compactification of a semisimple adjoint group, we outline several connections to Poisson geometry and to varieties of Lagrangian subalgebras. This survey is intended to be accessible to readers without an extensive background in algebraic geometry.