The Ulysses dust experiment is intended to provide direct observations of dust grains with masses between 10(-16) g and 10(-6) g in interplanetary space, to investigate their physical and dynamical properties as functions of heliocentric distance and ecliptic latitude. Of special interest is the question of what portion is provided by comets, asteroids and interstellar particles. The investigation is performed with an instrument that measures the mass, speed, flight direction and electric charge of individual dust particles. It is a multicoincidence detector with a mass sensitivity 10(6) times higher than that of previous in-situ experiments which measured dust in the outer solar system. The instrument weighs 3.8 kg, consumes 2.2 W, and has a normal data transmission rate of 8 bits/s in nominal spacecraft tracking mode. On 27th October 1990 the instrument was switched-on. The instrument was configured to flight conditions and science data collection started immediately. In the period to 13th January 1991 at least 44 dust impacts have been recorded. Flux values are given covering the heliocentric distance range from 1.04 to 1.7 AU.