The implant has two parts with the former oriented in the posterior-anterior direction of the spine and the latter perpendicular to the former, the parts being connected by a transition portion (5). The front face of the latter part (1a) has a protrusion, which is received by the former part (1b), thereby making the parts male and female implants, respectively. The shape and the dimensions of the elastic tabs of the female implant making them able to permit insertion of the protrusion of the male implant into the receiver. The ends of the elastic tabs are inserted into the receiving seats in order to achieve and maintain a connection of the two implants. Independent claims are also included for the following: (a) an instrument set for fitting an Intersomatic implant (b) a tool to introduce Intersomatic implant into a receiving seat formed in an intervertebral disc (c) a method of engaging male and female implants.
