The joint between the atlas and axis is:
First cervical vertebra is known as Atlas.
Second cervical vertebra is known as Axis.

Special joint between Atlas, Axis and Occipital bone:

Atlanto-Occipital joint:

It is a synovial joint - ellipsoid type.
Allows ﬂexion and extension of head on neck (as like nodding up and down).


Atlanto-Axial joint:

It is a pivot type of joint.
Allows rotatory movement of head on neck (as like saying 'NO' - right and left rotation).
The dens of axis forms a pivot, around which the atlas rotates, permitting rotatory motion of  neck possible.
Ball and socket joint
Closely related to the first cervical nerve
Allows rotation of the head
Supported by the alar ligaments