A spine stabilization device, comprising: - An interbody spacer shaped to be inserted between a vertebral body of an upper vertebra and a vertebral body of a lower vertebra, and comprising a top surface oriented towards the lower endplate of the vertebral body of the upper vertebra and a bottom surface oriented towards the upper endplate of the vertebral body of the lower vertebra; and - A fixation device comprising at least one anchor, the anchor comprising an anchoring material portion (31, 71) that is configured to be introduced, in a liquid state, into bone tissue of at least one of the vertebral body of the upper vertebra and of the vertebral body of the lower vertebra, to thereby infiltrate the bone tissue, and to harden thereafter so as to fix the support portion to the vertebral body, wherein, the fixation device further comprises a support portion securing the interbody spacer against escaping from between the vertebral bodies of the upper and lower vertebra in a direction towards the fixation device, the support portion shaped to rest against an anterior or anteriolateral or lateral or posteriolateral or posterior end face of the interbody spacer, - and in that the fixation device comprises a plurality of fasteners, the fasteners comprising an anchoring portion and a retaining projection (24, 58, 73), wherein the anchoring portion is equipped to anchor in the vertebral body of the upper or lower vertebra with the aid of the anchoring material portion and to thereby constitute one of the anchors, and wherein the retaining projection projects from an anchoring portion axis towards a median plane of the interbody spacer to support the interbody spacer against escaping from between the vertebral bodies. - An interbody spacer shaped to be inserted between a vertebral body of an upper vertebra and a vertebral body of a lower vertebra, and comprising a top surface oriented towards the lower endplate of the vertebral body of the upper vertebra and a bottom surface oriented towards the upper endplate of the vertebral body of the lower vertebra; and - A fixation device comprising at least one anchor, the anchor comprising an anchoring material portion (31, 71) that is configured to be introduced, in a liquid state, into bone tissue of at least one of the vertebral body of the upper vertebra and of the vertebral body of the lower vertebra, to thereby infiltrate the bone tissue, and to harden thereafter so as to fix the support portion to the vertebral body, wherein, the fixation device further comprises a support portion securing the interbody spacer against escaping from between the vertebral bodies of the upper and lower vertebra in a direction towards the fixation device, the support portion shaped to rest against an anterior or anteriolateral or lateral or posteriolateral or posterior end face of the interbody spacer, the fixation device further comprises a support portion securing the interbody spacer against escaping from between the vertebral bodies of the upper and lower vertebra in a direction towards the fixation device, the support portion shaped to rest against an anterior or anteriolateral or lateral or posteriolateral or posterior end face of the interbody spacer, - and in that the fixation device comprises a plurality of fasteners, the fasteners comprising an anchoring portion and a retaining projection (24, 58, 73), wherein the anchoring portion is equipped to anchor in the vertebral body of the upper or lower vertebra with the aid of the anchoring material portion and to thereby constitute one of the anchors, and wherein the retaining projection projects from an anchoring portion axis towards a median plane of the interbody spacer to support the interbody spacer against escaping from between the vertebral bodies.