Ganymede presents a unique example of an internally magnetized moon whose intrinsic magnetic field excludes the plasma present at its orbit, thereby forming a magnetospheric cavity. We describe some of the properties of this mini-magnetosphere, embedded in a sub-Alfvénic flow and formed within a planetary magnetosphere. A vacuum superposition model (obtained by adding the internal field of Ganymede to the field imposed by Jupiter) organizes the data acquired by the Galileo magnetometer on four close passes in a useful, intuitive fashion. The last field line that links to Ganymede at both ends extends to ~2 Ganymede radii, and the transverse scale of the magnetosphere is ~5.5 Ganymede radii. Departures from this simple model arise from currents flowing in the Alfvén wings and elsewhere on the magnetopause. The four passes give different cuts through the magnetosphere from which we develop a geometric model for the magnetopause surface as a function of the System III location of Ganymede. On one of the passes, Ganymede was located near the center of Jupiter's plasma disk. For this pass we identify probable Kelvin-Helmholtz surface waves on the magnetopause. After entering the relatively low-latitude upstream magnetosphere, Galileo apparently penetrated the region of closed field lines (ones that link to Ganymede at both ends), where we identify predominantly transverse fluctuations at frequencies reasonable for field line resonances. We argue that magnetic field measurements, when combined with flow measurements, show that reconnection is extremely efficient. Downstream reconnection, consequently, may account for heated plasma observed in a distant crossing of Ganymede's wake. We note some of the ways in which Ganymede's unusual magnetosphere corresponds to familiar planetary magnetospheres (viz., the magnetospheric topology and an electron ring current). We also comment on some of the ways in which it differs from familiar planetary magnetospheres (viz., relative stability and predictability of upstream plasma and field conditions, absence of a magnetotail plasma sheet and of a plasmasphere, and probable instability of the ring current).