Explore the concept of rank in 3-manifold groups in this advanced mathematics lecture. Delve into the definition of rank as the minimal number of elements needed to generate a group, with a specific focus on its application to 3-manifold groups. Examine the relationship between rank and Heegaard genus, and investigate the work of Abert-Nikolov connecting rank growth in cover towers to the "cost" of measured equivalence relations. Learn about research by the speaker and Souto on ranks of mapping tori with large curve complex translation distance, as well as geometric decompositions of thick hyperbolic 3-manifolds with bounded rank. Gain insights into this complex mathematical topic through a comprehensive 51-minute presentation delivered at the Workshop on Groups around 3-Manifolds, hosted by the Centre de recherches mathématiques (CRM).