A modular intervertebral implant (1), particularly an artificial intervertebral disk having a central axis (2) and comprising a first and a second component (3; 4) being mutually connectable in a ball-joint like manner, whereby A) the first component (3) is provided with an apposition area (5) which is apt for abutment to an end plate of a first adjoining vertebral body, said first component (3) being further provided with a concave spherical articulation surface (9) which has a radius R; B) the second component (4) is provided with an apposition area (6) which is apt for abutment to an end plate of a second adjoining vertebral body, said second component (4) being further provided with a convex spherical articulation surface (10) having the same radius R as the concave spherical articulation surface (9); C) the first component (3) has a maximum height H1 and the second component (4) has a maximum height H2, such that a maximum overall height H < (H1 + H2) results for the assembled intervertebral implant (1); and D) said intervertebral implant (1) has a centre of rotation RZ which has a shortest distance A to the second apposition area (6), said shortest distance A being equal to the absolute value of (H2 - R); and whereby E) the first component (3) is selected from a first kit of at least M = 2 first components (3) with different maximum heights H1; and F) the second component (4) is selected from a second kit of at least N = 2 second components (4) with different maximum heights H2; such permitting G) a selection of the distance A of the centre of rotation RZ of the so assembled intervertebral implant (1).