This volume contains a selection of papers based on presentations given at the S. P. Novikov seminar held at the Steklov Mathematical Institute in Moscow. Topics and speakers were chosen by the well-kwn expert, S. P. Novikov, one of the leading mathematicians of the twentieth century. His diverse interests are the tradition of the seminar and are reflected in the topics presented in the book. The book begins with Novikov's paper analyzing the position of mathematics and theoretical physics at the beginning of the new millennium. Following is an interview with Novikov published in the Newsletter of the European Mathematical Society presenting the genesis of many of his ideas and his scientific school. The remaining articles address topics in geometry, topology, and mathematical physics. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.