A remotely operable underwater drilling system for use with a drill string comprising at least one drill rod and for use with an inner core barrel which is adapted to be contained within an interior of the drill string, the drilling system comprising: (a) a frame; (b) a deployment connector attached to the frame, for connecting the drilling system with a deployment cable so that the drilling system may be suspended from the deployment cable in a body of water; (c) an adjustable support mechanism attached to the frame, for enabling the drilling system to be supported on an underwater ground surface at a substantially level orientation; (d) a mast structure mounted on the frame, wherein the mast structure defines a drilling axis for the drill string; (e) a drill head mounted on the mast structure such that the drill head is aligned with the drilling axis and longitudinally reciprocable along the drilling axis, wherein the drill head has an upper drill head end and a lower drill head end, wherein the drill head defines a drill head bore extending fully through the drill head from the upper drill head end to the lower drill head end, wherein the drill head bore is substantially coaxial with the drilling axis, and wherein the drill head is comprised of: (i) a drill head connector for connecting the drill head with the drill string along the drilling axis; and (ii) a drill head bore closure device adjacent to the upper drill head end, wherein the drill head bore closure device is actuatable between a closed position in which the drill head bore is closed and an open position in which the drill head bore is open, and wherein the inner core barrel may be inserted into and removed from the interior of the drill string through the drill head bore when the drill head is connected with the drill string and the drill head bore closure device is actuated to the open position; and (f) a clamping mechanism mounted on the mast structure, for supporting the drill string along the drilling axis when the drill head is not connected with the drill string. (a) a frame; (b) a deployment connector attached to the frame, for connecting the drilling system with a deployment cable so that the drilling system may be suspended from the deployment cable in a body of water; (c) an adjustable support mechanism attached to the frame, for enabling the drilling system to be supported on an underwater ground surface at a substantially level orientation; (d) a mast structure mounted on the frame, wherein the mast structure defines a drilling axis for the drill string; (e) a drill head mounted on the mast structure such that the drill head is aligned with the drilling axis and longitudinally reciprocable along the drilling axis, wherein the drill head has an upper drill head end and a lower drill head end, wherein the drill head defines a drill head bore extending fully through the drill head from the upper drill head end to the lower drill head end, wherein the drill head bore is substantially coaxial with the drilling axis, and wherein the drill head is comprised of: (i) a drill head connector for connecting the drill head with the drill string along the drilling axis; and (ii) a drill head bore closure device adjacent to the upper drill head end, wherein the drill head bore closure device is actuatable between a closed position in which the drill head bore is closed and an open position in which the drill head bore is open, and wherein the inner core barrel may be inserted into and removed from the interior of the drill string through the drill head bore when the drill head is connected with the drill string and the drill head bore closure device is actuated to the open position; and (i) a drill head connector for connecting the drill head with the drill string along the drilling axis; and (ii) a drill head bore closure device adjacent to the upper drill head end, wherein the drill head bore closure device is actuatable between a closed position in which the drill head bore is closed and an open position in which the drill head bore is open, and wherein the inner core barrel may be inserted into and removed from the interior of the drill string through the drill head bore when the drill head is connected with the drill string and the drill head bore closure device is actuated to the open position; and (f) a clamping mechanism mounted on the mast structure, for supporting the drill string along the drilling axis when the drill head is not connected with the drill string.