Explore Helly graphs and injective metric spaces in this 42-minute lecture from the Workshop on Cube Complexes and Combinatorial Geometry. Delve into basic definitions, elementary properties, and simple examples of these mathematical concepts. Focus on nonpositive features, including local properties, bicombings, and classification of isometries. Discover various rich constructions of such spaces, often associated with groups of geometric nature like hyperbolic groups, braid groups, mapping class groups, and higher rank lattices. Gain insights from Thomas Haettel's fourth installment in the series on Helly graphs and injective metric spaces, presented at the Centre de recherches mathématiques (CRM).