Embedding problem between right-angled Artin groups

Given a graph $\mathrm{\Gamma }$, the right-angled Artin group $A(\mathrm{\Gamma })$ is given by the presentation $⟨u\in V(\mathrm{\Gamma })\mid [u,v]=1,\{u,v\}\in E(\mathrm{\Gamma })⟩$. The Embedding Problem in right-angled Artin groups asks, given two finite graphs $\mathrm{\Phi },\mathrm{\Psi }$, how to determine whether or not $A(\mathrm{\Phi })$ is isomorphic to a subgroup of $A(\mathrm{\Psi })$. These are the notes of a mini-course given at the CIRM in April 2022, dedicated to a geometric point of view on this embedding problem, based on quasi-median graphs.