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This book addresses a broad range of problems related to observed manifestations of chaotic motions in galactic and stellar objects, by invoking basic theory, numerical modeling, and observational evidence. For the first time, methods of stochastic dynamics are applied to actually observed astronomical objects, e.g. the gaseous disc of the spiral galaxy NGC 3631. In the latter case, the existence of chaotic trajectories in the boundary of giant vortices was recently found by the calculation of the Lyapunov characteristic number of these trajectories. The reader will find research results on the peculiarities of chaotic system behaviour; a study of the integrals of motion in self-consistent systems; numerical modeling results of the evolution process of disk systems involving resonance excitation of the density waves in spiral galaxies; a review of specific formations in stars and high-energy sources demonstrating their stochastic nature; a discussion of the peculiarities of the precessional motion of the accretion disk and relativistic jets in the double system SS 433; etc. TOC:Stochastic Appearance in Stars and High Energy Sources.- Observational Manifestations of Precession of Accretion Disk in the SS 433 Binary System.- Orbits and Integrals in Self-consistent Systems.- Observational Manifestations of Chaos in the Gaseous Disk at the Grand Design Spiral Galaxy NGC 3631.- Observing Chaos in External Spiral Galaxies.- Spectral Analysis of Orbits via Discrete Fourier Transforms.- Should Elliptical Galaxies be Idealised as Collisionless Equilibria?- How Important are the Equations of Motion in a Chaotic System?- Resonantly Excited Non-linear Density Waves in Disk Systems.