Geometry is the study of figures in a space of a given number of dimensions and of a given type. Modern Geometry is a rapidly developing field, which vigorously interacts with other disciplines such as physics, analysis, biology, number theory, to name just a few. In recent years geometers encountered a significant number of groundbreaking results and fascinating applications. From progress in the Poincaré conjecture, geometric representation theory, quantization, to the mirror symmetry, string theory, applications in optics, biology, quantum computing — the ubiquity of geometry is impossible to overestimate. People in our group work in several important directions. We maintain strong contacts and collaboration with other groups in our department.