This survey is based on lectures the author has given at various times at the Independent University of Moscow, Moscow State University, the Steklov Mathematical Institute (Moscow and St. Petersburg branches), the Technical University of Berlin, the Ruhr University of Bochum, the Lorand Eötvos University of Budapest, the University of Geneva, the University of Heidelberg, the University of Ljubljana, the University of Siegen, the University of Uppsala, the University of Warsaw and the University of Zagreb. He gratefully acknowledges the support provided by INTAS grant no. YSF-2002-393, by the Russian Foundation for Basic Research, grants nos. 05-01-00993, 04-01-00682 and 06-02-72551-NCNILa, President of Russian Federation grants MD-3938.2005.1, MD-4729.2007.1 and NSH-4578.2006.1, and by the Pierre Deligne fund based on his 2004 Balzan prize in mathematics.
The preliminary version was prepared in January 2002 after a series of lectures at the Universities of Aberdeen, Cambridge, Edinburgh and Manchester, sponsored by the London Mathematical Society via the programme ‘Invitation of young Russian mathematicians’. The author would like to acknowledge all these institutions for their hospitality and personally thank P. M. Akhmetiev, V. M. Buchstaber, A. V. Chernavskiy, Y. Choi, P. Eccles, K. E. Feldman, A. T. Fomenko, U. Koschorke, M. Kreck, W. B. Lickorish, A. Haefliger, R. Levy, S. Mardesic, A. S. Mischenko, N. Yu. Netsvetaev, V. M. Nezhinskiy, M. M. Postnikov, E. Rees, D. Repovs, E. V. Schepin, Yu. P. Solovyov, A. Szücs, V. A. Vassiliev, O. Ya. Viro, C. Weber, M. Weiss, G. Ziegler and H. Zieschang for their invitations and useful discussions.