Dust was observed in the Jovian magnetosphere with the dust detector onboard the Galileo spacecraft. Measurements have been obtained inside a distance of about 100R(J) from Jupiter's center (Jupiter radius, R-J = 71,492 km) during a period of 20 days covering Galileo's closest approach to Ganymede on September 6, 1996, 18:59 UTC. At least three types of dust particles have been detected: (1) submicrometer-sized particles found throughout the Jovian system with high and variable impact rates, implying that the particles' trajectories are strongly affected by the interaction with the Jovian magnetic field; (2) concentrations of small dust impacts at the time of Ganymede closest approach, which could be secondary ejecta particles generated upon impact of other particles onto Ganymede's surface; and (3) micrometer-sized dust particles, which could be on bound orbits about Jupiter, and which are concentrated in the inner Jovian system inside about 20R(J) from Jupiter.