This lecture explores "The Boundary of the Limit Cone of Anosov Groups" presented by François Guéritaud as part of the "New Trends in Teichmüller Theory" program at the International Centre for Theoretical Sciences. Delve into advanced concepts at the intersection of Higher Teichmüller theory, Anosov representations, and geometric group theory. The talk contributes to the two-week thematic program focusing on recent developments in Teichmüller theory, which also covers metric theory of Teichmüller spaces, infinite-type surfaces, and relations with anti-de Sitter geometry. Drawing from complex analysis, hyperbolic geometry, dynamics, and other mathematical fields, this presentation offers valuable insights for researchers and advanced students interested in the cutting-edge developments of this rich mathematical domain.