The monograph sets out the theory of the motion of neutral gas in the atmospheres of comets. The purpose of the monograph is to give the necessary apparatus for calculating the physical conditions in various layers of the neutral gas atmosphere. Identification of parent molecules by observed radicals is considered; the transition of neutrals to the atmosphere, the movement of gases in the area where collisions are significant, the heating of gas in this area due to photodissociation and the presence of dust, the behavior of dust particles (ejected from the core and newly formed in the atmosphere by condensation or photopolymerization) in a dusty atmosphere; anisotropization of temperatures in the region of transition to the free molecular mode; gas kinetics in the collisionless region. The case when a free molecular flow regime is carried out in the entire cometary atmosphere has been studied taking into account the rotation of the nucleus and the kinetics of photodissociation. For the most common cases in practice, relations have been obtained that allow calculating the distribution of surface brightness in images of comets; describes the methodology for performing such calculations for an arbitrary case. The book is designed for scientists of astronomical institutions and universities, students and graduate students specializing in astrophysics.