The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy is organizing a Advanced School and Workshop on Geometric Group Theory and Low-dimensional Topology: Recent Connections and Advances, to be held at ICTP, Trieste, Italy, 23 May - 3 June 2016. The themes that the Advanced School and Workshop will focus are the very cutting edge of research in Geometry and Topology and its connections wih Group Theory. The motivation for this advanced school is to expose students, postdocs and researchers to various key roles that geometric group theory has played in recent advances in low-dimensional topology and geometry. These include (but not limited to) the role of virtually special groups, representations of Kleinian groups in SL(2,C) and generalizations (e.g. Higher Teichmuller Theory), the Mapping Class Group and its recent role in low dimensional geometry and topology and group theoretic connections with Heegaard Floer theory through left-orderability. TOPICS COVERED: Virtually Special Groups and Cube Complexes Geometry and Topology of Hyperbolic 3-Manifolds, the Mapping Class Group and Curve Complex Higher Teichmuller Theory and Geometric Structures Left Orderability, L-spaces and Applications to 3-Manifolds Dynamics on Teichmuller Space and Moduli Space