General

Unity uses 3 rotation systems.

1. Euler Angers - rotation about x, y, z axis
2. Angle Axis - A normalized Vector3 representing the axis about which to rotate by float angle amount
3. Quaternions

// Convert from Quaternion to Euler:
Vector3 inEuler = quaternionRotation.eulerAngles;
 
// Convert Euler to Quaternion
Quaternion inQuaternion = Quaternion.Euler(inEuler);
 
// To Angle-Axis
Quaternion randomQuaternion = Random.rotation;
float angle;
Vector3 axis;
 
randomQuaternion.ToAngleAxis(out angle, out axis);
 
// And back
Quaternion rotation = Quaternion.AngleAxis(angle,axis);