- A system comprising - a self-climbing structure for a vertical or near-vertical concrete surface, the self climbing structure comprising frames, (4a, 4b and 4c), and - an anchor assembly, the anchor assembly comprising - a plurality of metal inserts fixable to an internal reinforcement of a segment of the vertical or near-vertical concrete surface, which is configured to form openings in a wall of the segment, and distributable at different heights on the vertical or near-vertical concrete surface, - interlocking spikes, suitable for insertion and coupling in the metal inserts, and located in the frames (4a, 4b and 4c) of the self-climbing structure, the interlocking spikes being provided with means of horizontal and vertical displacement and with means of approach and distancing in relation to the vertical or near-vertical concrete surface, characterized in that the interlocking spikes comprising - an inner shaft, provided with a spherical end, - a main body, enveloping the spherical end of the inner shaft, and provided with free rotation movement in relation to it, the lower part of the main body being semi-circular, and - end plates attached to the front and rear ends of the main body, and which protrude from the main body at the bottom. - a self-climbing structure for a vertical or near-vertical concrete surface, the self climbing structure comprising frames, (4a, 4b and 4c), and - an anchor assembly, the anchor assembly comprising - a plurality of metal inserts fixable to an internal reinforcement of a segment of the vertical or near-vertical concrete surface, which is configured to form openings in a wall of the segment, and distributable at different heights on the vertical or near-vertical concrete surface, - interlocking spikes, suitable for insertion and coupling in the metal inserts, and located in the frames (4a, 4b and 4c) of the self-climbing structure, the interlocking spikes being provided with means of horizontal and vertical displacement and with means of approach and distancing in relation to the vertical or near-vertical concrete surface, characterized in that the interlocking spikes comprising - an inner shaft, provided with a spherical end, - a main body, enveloping the spherical end of the inner shaft, and provided with free rotation movement in relation to it, the lower part of the main body being semi-circular, and - end plates attached to the front and rear ends of the main body, and which protrude from the main body at the bottom. the anchor assembly comprising - a plurality of metal inserts fixable to an internal reinforcement of a segment of the vertical or near-vertical concrete surface, which is configured to form openings in a wall of the segment, and distributable at different heights on the vertical or near-vertical concrete surface, - interlocking spikes, suitable for insertion and coupling in the metal inserts, and located in the frames (4a, 4b and 4c) of the self-climbing structure, the interlocking spikes being provided with means of horizontal and vertical displacement and with means of approach and distancing in relation to the vertical or near-vertical concrete surface, - a plurality of metal inserts fixable to an internal reinforcement of a segment of the vertical or near-vertical concrete surface, which is configured to form openings in a wall of the segment, and distributable at different heights on the vertical or near-vertical concrete surface, - interlocking spikes, suitable for insertion and coupling in the metal inserts, and located in the frames (4a, 4b and 4c) of the self-climbing structure, the interlocking spikes being provided with means of horizontal and vertical displacement and with means of approach and distancing in relation to the vertical or near-vertical concrete surface, characterized in that the interlocking spikes comprising - an inner shaft, provided with a spherical end, - a main body, enveloping the spherical end of the inner shaft, and provided with free rotation movement in relation to it, the lower part of the main body being semi-circular, and - end plates attached to the front and rear ends of the main body, and which protrude from the main body at the bottom. - an inner shaft, provided with a spherical end, - a main body, enveloping the spherical end of the inner shaft, and provided with free rotation movement in relation to it, the lower part of the main body being semi-circular, and - end plates attached to the front and rear ends of the main body, and which protrude from the main body at the bottom.