Spinning top fixed point I have seen many explanations about the movement of a spinning top. The explanations were in a varied level, from basic newtonian mechanics to Lagrangian formalism. But I do not understand why some people consider different fixed points. In same cases it is the point of contact with the surface and others consider some point in the "middle" of the spinning top.  My question is whether this ambiguity is a misinterpretation (of those authors), a free choice to describe the movement or a difference caused from different spinning tops?
 A: When calculating rotation problems, with torques and suchlike, it is necessary to choose an origin for the coordinate system. This choice is ultimately arbitrary since the equation of motions are equivalent, so the origin is generally chosen to be what makes the equations the simplest. If an object is fixed to rotate around a pivot, then choosing the origin to be on the pivot will make the torque from the force exerted by the pivot on the object vanish, while if the object is freely rotating in the air, usually the center of mass is the best choice because it moves like a point particle does and because gravity acts from the center of mass. So the choice of origin for calculating torques and angular momenta is fundamentally arbitrary (although if you do something perverse, like having the origin accelerate, then you also have to account for that kind of thing through fictitious forces.)
There's a different matter of trying to assign a spinning object an axis that it is spinning around. In the simplest cases which are typically encountered, there is an obvious center of rotation. A gear rotates around the axle since when you spin it back and forth, the axle remains stationary. When you chuck some rigid object in the air, the center of mass moves in a parabolic motion, while every other point moves in a more complicated way. In the center of mass frame, the COM is fixed while the rest of the object rotates around it, so one can say the object is rotating about its center of mass.
In more complicated cases, assigning an axis to a motion is a bit of an ill defined problem. If you go look at a car driving down a highway, at each instant, in the frame of the ground, it is the bottom of the wheel which is stationary, and the rest of the wheel is rotating about it. So at each instant one might say that the wheel is actually rotating about its bottom. But if you take the frame of the car, then the wheel is obviously spinning about its axle. If you take a phone-shaped object and throw it spinning in the air, generally it will have a very complicated motion. Even if you subtract the motion of the center of mass out, then the axis of points which are at that moment stationary will move around wildly, and will correspond to different parts of the object at various times, a bit like the wheel considered from the ground's frame. The angular momentum will also point in yet another direction and the whole situation is a bit of a mess. So if you want to actually assign an axis of rotation to a rotating object, rather than just choose an origin for the purposes of calculation, that is generally ambiguous.
A: When a top rotates, it rotates about its centre of mass. The centre of the mass is a point on the axis of rotation. Since the axis is also stationary as is the centre of mass, therefore all the points in the axis are eligible to be considered fixed about which the top is rotating. 
Besides,I would prefer to use the term axis instead of a fixed point. 
A: Spinning of a top about a fixed point is different from spinning in space or about center of mass. When a top lean certain angle it slips like a slanting ladder because of lack of sufficient frictional force. nutation is observed in the case of a top when there is slip at the contact point.
