Baikal Summer School on Physics of Elementary Particles and AstroPhysics organized by Joint Insitute for Nuclear Research (Dubna, Russia) and Irkutsk State University (Irkutsk) was held in a pictorial place of National Park on the Baikal Lake in a small village "Bol'shie Koty" from 11 till 16 of july 2004. 25 participants from Irkutsk State University and Joint Institute for Nuclear Research attended this school. The Baikal Summer is a natural step of previous schools and conferences organized in past by JINR, ISU and Insitute of Mathematics (Novosibirsk) headed by acadimican D.V.Shirkov. Previous conferences attracted many bright names as Nobel prize winners I.M.Frank and P.A. Cherenkov, M.G. Mesheryakov and many others. We hope to continue this tradition and make the school again attractive for russian and international physicists. Financial support of Russian Fond for Fundamental Research, JINR and Irkutsk administration made this school of 2004 possible.