This volume offers deep insight into the methods and concepts of a very active field of mathematics that has many connections with physics. Researchers and students will find it to be a useful source for their own investigations, as well as a general report on the latest topics of interest. Presented are contributions from several specialists in differential geometry and mathematical physics, collectively demonstrating the wide range of applications of Lorentzian geometry, and ranging in character from research papers to surveys to the development of new ideas. This volume consists mainly of papers drawn from the conference “New Developments in Lorentzian Geometry' (held in November 2009 in Berlin, Germany), which was organized with the help of the DFG Collaborative Research Center's “SFB 647 Space-Time-Matter' group, the Berlin Mathematical School, and Technische Universitat Berlin.