Tropical and non-Archimedean geometry (1)

This will be an introductory overview of the relationship between tropical and non-Archimedean analytic geometry for closed subvarieties of toric varieties. In particular, I will focus on the relationship between non-Archimedean skeletons and tropicalizations. The final goal will be a discussion of the tropicalization of the moduli space $\overline{M}_{0,n}$ of rational stable curves in the classical framework, i.e. via an embedding into a toric variety.