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 (Z); 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 (XZ) running parallel to the hinge axis (Z) and is adjustable in a second plane (YZ) running at a right angle to the first plane (XZ) 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 (Z); 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 (XZ) running parallel to the hinge axis (Z) and is adjustable in a second plane (YZ) running at a right angle to the first plane (XZ) 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 . <EOS>