The gearbox (it is really just a gearbox, not a transmission) is filled with SAE 10W-30 engine oil, about 65cc (2.2 oz). It is factory-filled for the lifetime of the mower, and there is no service ever required.
Should the gearbox ever develop a leak, the cover and o-ring can be removed, then the gear box inverted (input shaft facing down) so the open side of the gear box is level with the ground. Fill with fresh SAE 10W30 oil so the level of oil is about 18-20 mm from the top of the gearbox case. Replace the o-ring and install the cover and four bolts. Torque them (important!) to 6.5~8.7 ft-lbs.