Constructive field theory took shape as an independent direction in the 60s guides, and in the last decade significant results have been obtained in it. The proposed collection is based on lectures given at the International School of Mathematical Physics. Among the authors of the articles are well-known specialists actively working in this field - J. Glimm, A. Jaffe, E. Nelsoi and others. Compile a collection of theoretical physicists and mathematicians interested in the problems of physics.