The state of the main problems of heat and mass transfer, which takes place in many modern technical devices and technological processes of most industries, is described. The first section covers the main provisions of the theory of thermal conductivity, convective and radiant heat transfer, as well as special issues of heat transfer. The second section discusses the laws of mass conductivity and interrelated heat and mass conductivity, convective mass transfer and heat and mass transfer when the aggregate state of a substance changes.