1. An apparatus (1) for treating fluids (5) in the form of drinking water, service water, waste water or aqueous solutions by producing corona discharges in a
fluid volume (6), wherein the apparatus has an electrode assembly (2) with at least one cylindrical cathode (3) and at least one linear anode (4) arranged in the interior of the cathode (3) and at a distance from the cathode (3), and a high voltage unit (7) to produce high-voltage pulses (8), wherein the highvoltage unit (7) is connected to the electrode assembly (2) in order to apply high-voltage pulses (8) to the at least one anode (4), and wherein the electrode assembly (2) is configured to accommodate the fluid (5) to be treated in the space between the at least one cathode (3) and the at least one anode (4), wherein the high-voltage unit (7) is configured to produce high-voltage pulses (8) with pulse rise times within a range of 1 to 40 nanoseconds and a pulse duration within a range of 50 to 400 nanoseconds, characterized in that a plurality of dielectric surface elements (19, 21) extend radially toward the associated cylindrical cathode (3) starting from the at least one linear anode (4).