The coffee maker comprises a brewing head (4) which heats the water and is guided up and down in guide columns (5) in a housing (11). A holder (10) for the ground coffee can be moved horizontally from the brewing position underneath the brewing head into a filling position when the brewing head is moved upwards. The ground coffee holder is a filter pan for a filter or filter bag for the pressureless production of the filter coffee. A screen holder (12) for ground espresso coffee can be placed in the filter bag to produce espresso coffee under pressure.