The Pioneer 11 spacecraft encounter with Saturn (closest approach September 1,1979) has resulted in the discovery of a fully developed magnetosphere with high-energy trapped radiation around Saturn, as reported in Science, 207, 400--453, 1980, by several investigators with charged-particle instruments on the spacecraft. The present paper contains in detail the final energetic charged-particle measurements and new observations obtained from the University of Chicago instrumentation on Pioneer 11, including the overall characteristics of the trapped electron, proton, and helium radiation, which was found to lie inside ~20 Saturn radii (Rs) from the planet, and the regions extending outward to beyond the planetary bow shocks and into the interplanetary medium. For analytical purposes we divided that magnetosphere into an inner magnetosphere (<5Rs), where the intensity profiles displayed the near-axial symmetry characteriscis of the sipole magnetic field alignment with the spin axis, and an outer magnetosphere whose characteristic on the sunward side inbound were significantly different from the dawn side out-bound, indicative of a possible magnetotial but with no dramatic evidence in the charged-particle data for an equatorial current sheet, as observed at Jupiter. The intensities and energy ranges of the protons and electrons were intermediate between the levels found previously at Jupiter by Pioneer 10 and 11 and at earth. Each spectra for protons and electrons and relative abundances of protons and helium nuclei are presented along with the average characteristics of particle anisotropies. At the time of encounter the magnetosphere was immersed in intense fluxes of electrons, protons, and helium nuclei of solar flare origin which are shown to penetrate from 1 Rs to 1 10 Rs into the magnetosphere, where they dominated the flux levels in the far outer magnetosphere. A corotation anisotropy has been measured at the proton energy ~1 MeV in the rotating magnetosphere after correcting the observed unidirectional anisotropy for the radial gradient of the proton flux. The principal focus of the paper is on the analysis of the trapped radiation in the inner magnetosphere, where the radiation reaches high intensity, and has a high degree of symmetry in the L shells around Saturn. Consequently, the absorption signatures in the radiation intensity profiles produced by rings and moons of Saturn can be analyzed quantitatively. Among other results the observation of the charged-particle absorption features have led to the discovery of satellite 1979 S2 at L=2.53, which corresponds with the optically detected 1979 S1. A concentration of matter probably located at a Lagrangian point in the orbital range of Mimas, and the identification of narrow rings of matter and one or more satellites inside the radiation range of the F ring dicovered by the optical-imaging investigators. It is pointed out that these discoveries will provide important tests for models of accretion of matter, satellite formation and the stability of narrow rings near planets. From the discrete character of the absorption symmetry it is shown that except for two extremely narrow intervals of Saturn's longitude, the equatorial offset of the dipole magnetic moment must be ≲0.01 Rs. The inward diffusion coefficients for protons and electrons have been determined from the above absorption regions, especially at Mimas. Some questions are considered which may be resolved by the forthcoming Voyager encounters with Saturn.