- Definition of Coxeter and Artin groups - What is a geometric action? - Definitions coming from this geometric action - Classification of regular polytopes and spherical Coxeter groups - Classification of euclidean Coxeter groups - Spherical and euclidean tilings - Equivalent definitions coming from Lie groups and algebras.

- The root system - The cosine matrix and the symmetric bilinear form - Classification of spherical and euclidean Coxeter groups coming from linear algebra - Tits representation - Properties of Tits representation - Historical remarks.

- Consequences of the faithfulness of Tits representation - The Tits cone - An explicit example - Cayley graphs and W-permutahedra - The Davis complex - The Davis complex with Moussong's metric.

- More on the Davis-Moussong complex - Explicit examples: spherical, euclidean, and hyperbolic - Piecewise euclidean metric spaces - CAT(0) spaces and groups - Coxeter groups are CAT(0) groups - The Word and Conjugacy Problems - Open questions on CAT(0) groups.

- Applying a metric perspective - Quasi-isometries and the Milnor-Svarc theorem - Fundamental observation - A second generation proofs in differential geometry - (Gromov) Hyperbolic spaces and groups - Hyperbolic Coxeter groups - Consequences of being a hyperbolic group - A theorem of Gromov and genesis of a new subfield in Mathematics...

- Braid group of an action - Complex reflection and braid groups - Shephard and Todd classification - BMR 1998 - Harm van der Lek 1983 - Artin groups - Salvetti and Deligne complexes: from Coxeter to Artin groups - Salvetti complex for the RAAGs - The K(\pi,1) conjecture - Problems related to Artin groups: linear groups, torsion-freeness, Word and Conjugacy Problems, K(\pi,1), CAT(0) - Application to RAAGs - (Application to) Small-type Artin groups - Coarser classifications up to quasi-isometry.