Book excerpt: The equilibrium properties of one-dimensional self-gravitating systems are investigated analytically. One-dimensional models are used to perform computer experiments tracing the evolution of stellar systems. The stationary solution of the Vlasov equation for a one-dimensional system of stars as computed for an interesting class of initial conditions is found to correspond to a minimum-energy configuration. The results of the numerical experiments are compared with theory. For initial energies far from the minimum equilibrium energy the system becomes unstable and breaks up into smaller clusters. A variational principle was applied to the one-dimensional stellar system to show that stationary distribution functions which decrease monotonically in going outward from the center of the system are stable. That other stationary distributions may be unstable is illustrated by means of computer experiments. The one-dimensional model is of interest as an approximation to the distribution of velocity and mass normal to the galactic plane of a greatly flattened galactic system. Observational results for the gravitational force normal to the galactic plane of the Galaxy agree with the results obtained from the one-dimensional model. Thermalization effects for systems containing small numbers of stars were investigated. The fluctuation of the kinetic energy was found to be inversely proportional to the square root of the number of particles in the system.