(Volume I).- § 1. Basic Concepts and Equations of Theory.- § 2. Equilibrium States of Collisionless Gravitating Systems.- § 3. Small Oscillations and Stability.- §4. Jeans Instability of a One-Component Uniform Medium.- §5. Jeans Instability of a Multicomponent Uniform Medium.- §6. Non-Jeans Instabilities.- § 7. Qualitative Discussion of the Stability of Spherical, Cylindrical (and Disk-Shaped) Systems with Respect to Radial Perturbations.- I Theory.- I Equilibrium and Stability of a Nonrotating Flat Gravitating Layer.- II Equilibrium and Stability of a Collisionless Cylinder.- III Equilibrium and Stability of Collisionless Spherically Symmetrical Systems.- IV Equilibrium and Stability of Collisionless Ellipsoidal Systems.- V Equilibrium and Stability of Flat Gravitating Systems.- References.- Additional References.

It would seem that any specialist in plasma physics studying a medium in which the interaction between particles is as distance-dependent as the inter­ action between stars and other gravitating masses would assert that the role of collective effects in the dynamics of gravitating systems must be decisive. However, among astronomers this point of view has been recog­ nized only very recently. So, comparatively recently, serious consideration has been devoted to theories of galactic spiral structure in which the dominant role is played by the orbital properties of individual stars rather than collec­ tive effects. In this connection we would like to draw the reader's attention to a difference in the scientific traditions of plasma physicists and astrono­ mers, whereby the former have explained the delay of the onset of controlled thermonuclear fusion by the "intrigues" of collective processes in the plasma, while many a generation of astronomers were calculating star motions, solar andlunar eclipses, and a number of other fine effects for many years ahead by making excellent use of only the laws of Newtonian mechanics. Therefore, for an astronomer, it is perhaps not easy to agree with the fact that the evolution of stellar systems is controlled mainly by collective effects, and the habitual methods of theoretical mechanics III astronomy must make way for the method of self-consistent fields.