A hinge for mounting a door or window sash to a frame, the hinge comprising: first and second hinge parts which are operatively connected to one another by an adjustment bolt so as to be rotatable about a common hinge axis; the first hinge part has a plate-shaped portion which is configured to interact in a fixedly and releasably connectable manner with a retaining piece configured for connection to the door or window sash or in the frame, and the second hinge part is configured for connection to the other of the door or window sash or the frame; the plate-shaped portion is oriented in a first plane running parallel to the hinge axis and is adjustable in a second plane running at a right angle to the first plane of the plate-shaped portion; a dual threaded grub screw having a first thread section screwed into a threaded bore of the retaining piece and a second thread section, having an opposite thread direction than the first thread section, screwed into a threaded opening of an intermediate piece, an axis of the dual threaded grub screw extending perpendicular to the plate-shaped portion; a clamping device comprising a clamping bolt and a sleeve arranged such that the plate-shaped portion and the intermediate piece are held together from one side with said clamping bolt and from the other side with said sleeve fitted onto the clamping bolt, and the intermediate piece and the plate-shaped portion are displaceable relative to each other by an eccentric on the clamping bolt; and the dual threaded grub screw has an inner head engagement portion that is accessible via an adjustment opening in the plate-shaped portion allowing a lateral adjustment of the first hinge part relative to the second hinge part. first and second hinge parts which are operatively connected to one another by an adjustment bolt so as to be rotatable about a common hinge axis; the first hinge part has a plate-shaped portion which is configured to interact in a fixedly and releasably connectable manner with a retaining piece configured for connection to the door or window sash or in the frame, and the second hinge part is configured for connection to the other of the door or window sash or the frame; the plate-shaped portion is oriented in a first plane running parallel to the hinge axis and is adjustable in a second plane running at a right angle to the first plane of the plate-shaped portion; a dual threaded grub screw having a first thread section screwed into a threaded bore of the retaining piece and a second thread section, having an opposite thread direction than the first thread section, screwed into a threaded opening of an intermediate piece, an axis of the dual threaded grub screw extending perpendicular to the plate-shaped portion; a clamping device comprising a clamping bolt and a sleeve arranged such that the plate-shaped portion and the intermediate piece are held together from one side with said clamping bolt and from the other side with said sleeve fitted onto the clamping bolt, and the intermediate piece and the plate-shaped portion are displaceable relative to each other by an eccentric on the clamping bolt; and the dual threaded grub screw has an inner head engagement portion that is accessible via an adjustment opening in the plate-shaped portion allowing a lateral adjustment of the first hinge part relative to the second hinge part.