A construction system, for landscape applications, indoor or outdoor privacy walls, stairs, privacy fences, mortar-less masonry walls, residential and commercial sound barriers, the construction system comprising: a plurality of core blocks (1, 6), each core block (1, 6) having: a front face; a rear face; a top face; a bottom face; a left side face; and a right side face, each core block (1, 6) having protrusions and grooves the top and bottom faces (9; 10) for interlocking the core blocks (1, 6) together in stacked rows with adjacent side faces, each core block (1, 6) having a slip molding axis and a uniform cross-sectional profile transverse to the slip molding axis, wherein the front, rear, top and bottom faces (7; 8; 9; 10) define the core cross-sectional profile; a plurality of fascia blocks (2, 3, 23), each fascia block having: a decorative exposed front face; a rear face; a top face; a bottom face; a left side face; and a right side face, wherein each fascia block has a slip molding axis and a uniform cross-sectional profile transverse to the slip molding axis, wherein the left and right side faces, the top and bottom faces (9; 10) define the fascia cross-sectional profile, and wherein each fascia block has a center of gravity located at an eccentric distance from the rear face; a plurality of connectors for supporting stacked rows of the fascia blocks (2, 3, 23) suspended on one of: the front faces; and the rear faces of the stacked rows of core blocks (1, 6), the connectors comprising: a horizontal ledge having a downward sloping surface, the horizontal ledge protruding from one of: the rear face of the fascia blocks (2, 3, 23); and the front face of the core blocks (1, 6); and a matching horizontal recess having a downward sloping surface, the horizontal recess disposed in one of: the front face of the core blocks (1, 6); and the rear face of the fascia block (2, 3, 23), wherein the fascia blocks (2, 3, 23) are each supported by their rear faces, by engagement of the downward sloping surfaces of the horizontal ledge and the matching horizontal recess, and the rear face of each fascia block is rotated into contact with the front face of the core blocks (1, 6), by the force of gravity acting on each fascia block through said center of gravity located at said eccentric distance from the rear face. a plurality of core blocks (1, 6), each core block (1, 6) having: a front face; a rear face; a top face; a bottom face; a left side face; and a right side face, each core block (1, 6) having protrusions and grooves the top and bottom faces (9; 10) for interlocking the core blocks (1, 6) together in stacked rows with adjacent side faces, each core block (1, 6) having a slip molding axis and a uniform cross-sectional profile transverse to the slip molding axis, wherein the front, rear, top and bottom faces (7; 8; 9; 10) define the core cross-sectional profile; a plurality of fascia blocks (2, 3, 23), each fascia block having: a decorative exposed front face; a rear face; a top face; a bottom face; a left side face; and a right side face, wherein each fascia block has a slip molding axis and a uniform cross-sectional profile transverse to the slip molding axis, wherein the left and right side faces, the top and bottom faces (9; 10) define the fascia cross-sectional profile, and wherein each fascia block has a center of gravity located at an eccentric distance from the rear face; a plurality of connectors for supporting stacked rows of the fascia blocks (2, 3, 23) suspended on one of: the front faces; and the rear faces of the stacked rows of core blocks (1, 6), the connectors comprising: a horizontal ledge having a downward sloping surface, the horizontal ledge protruding from one of: the rear face of the fascia blocks (2, 3, 23); and the front face of the core blocks (1, 6); and a matching horizontal recess having a downward sloping surface, the horizontal recess disposed in one of: the front face of the core blocks (1, 6); and the rear face of the fascia block (2, 3, 23), a horizontal ledge having a downward sloping surface, the horizontal ledge protruding from one of: the rear face of the fascia blocks (2, 3, 23); and the front face of the core blocks (1, 6); and a matching horizontal recess having a downward sloping surface, the horizontal recess disposed in one of: the front face of the core blocks (1, 6); and the rear face of the fascia block (2, 3, 23), wherein the fascia blocks (2, 3, 23) are each supported by their rear faces, by engagement of the downward sloping surfaces of the horizontal ledge and the matching horizontal recess, and the rear face of each fascia block is rotated into contact with the front face of the core blocks (1, 6), by the force of gravity acting on each fascia block through said center of gravity located at said eccentric distance from the rear face.