Building Bridges Between Algebra and Topology

This volume presents an elaborated version of lecture notes for two advanced courses:  (Re)Emerging methods in Commutative Algebra and Representation Theory  and  Building Bridges Between Algebra and Topology,  held at the CRM in the spring of 2015. Homological algebra is a rich and ubiquitous area; it is both an active field of research and a widespread toolbox for many mathematicians. Together, these notes introduce recent applications and interactions of homological method