The book describes the mathematical apparatus and some physical concepts that can be useful in the creation (modernization) of an intelligent transport system (ITS). The first edition was published in 2010 by the MIPT publishing house. Among other things, practical materials from A + C Consult (PTV Vision r) and Yandex.Traffic were added to this second edition. Designed for senior students and graduate students of physical and mathematical specialties (MIPT, NMU, Moscow State University, MSTU, HSE). It is recommended for researchers interested in mathematical modeling.