- This article reviews recent studies of morphology and dynamics of low and moderately high optical depth regions of the Saturnian ring system of discrete mutually gravitating particles with special emphasis on its fine-scale spiral structure (irregular cylindric structures of the order of or so). We explain the very existence and the value of the critical wavelength of the fine structure, arising due to classical Jeans instability of gravity perturbations, in a local version of kinetic stability theory. The same interpretation is suggested to explain the gravitational wakes in simplified N-body computer simulations in Hill's equations context of an orbiting patch of the ring. A self-consistent system of the Boltzmann kinetic equation with a Krook phenomenological integral of collisions and the Poisson equation is used to study the phenomenon. The simplified case of relatively rare collisions between identical particles is examined, when the collision frequency is smaller than (compared to) the orbital frequency. It is shown that there is a dominant Fourier mode of maximum instability of Jeans-type collective oscillations in Saturn's rings (and the associated number of spiral arms and the pitch angle). We again argue that sufficient velocity dispersion prevents the Jeans instability from occurring but inelastic interparticle collisions reduce the relative particle velocities so that the Jeans instability may be an effective generating mechanism for the recurrent fine structure of the ring system. The stability analysis presented here and N-body simulations in Hill's approximation by Salo (Nature 359 (1992) 619), Richardson (Monthly Notices Roy. Astron. Soc. 269 (1994) 493), Osterbart and Willerding (Planet. Space Sci. 43 (1995) 289), Sterzik et al. (Planet. Space Sci. 43 (1995) 259), and others, would have to be regarded as a prediction of the long-term recurrent, tightly wound spiral structure in the range of few tens to few hundreds meters in regions of Saturn's main A, B, and C rings with optical depth τ≲1 that could be compared to forthcoming in 2004 Cassini spacecraft high-resolution measurements.