The general idea of the Seminar: to have a place where young mathematicians of all levels could try themselves in independent math research. Here I would like to quote my teacher I.M.Gelfand who used to say that his seminar is destined for high school and college students, talented graduates and excellent professors. The science is developing fast. While a student learns the basic facts and notions, the new facts are discovered and new concepts are created. To enter the modern science is like to catch the train on full speed. So, the widely accepted principle: ``learn first, do creative work afterwards'' is doomed to fail. Rather you start to work on a new subject having only a minimal preliminary knowledge, hardly enough to understand (or, better to say, feel) the problem. The success of Moscow mathematical school (the word ``Moscow''is used here as a synonym to ``Russian'' or ``Soviet'') is certainly related to the existence of many good seminars for young mathematicians starting with so-called mathematical circles in best schools, colleges and universities and finishing by research seminars runned by great mathematicians. Of course, there is no guarantee that you will succeed in solving the long standing problem or invent a new fruitful theory which makes you famous. What can be guaranteed, is that you will get a really active knowledge of some basic notions, acquire some skill to guess and prove (or disprove) mathematical statements and will experience an incomparable joy of discovery.