The transparent Sun is modeled as a spherically symmetric and centrally condensed gravitational lens using recent standard solar model (SSM) data. The Sun's minimum focal length is computed to a refined accuracy of 23.5 +/- 0.1 AU, just beyond the orbit of Uranus. The Sun creates a single image of a distant point source visible to observers inside this minimum focal length and to observers sufficiently removed from the line connecting the source through the Sun's center. Regions of space are mapped where three images of a distant point source are created, along with their associated magnifications. Solar caustics, critical curves, and Einstein rings are computed and discussed. Extremely high gravitational lens magnifications exist for observers situated so that an angularly small, unlensed source appears near a three-image caustic. Types of radiation that might undergo significant solar lens magnifications, as they can traverse the core of the Sun, including neutrinos and gravitational radiation, are discussed.