Before talking about how a top keeps balance, we should clarify what a top is. Generally, tops have many shapes but the typical shape is conical or spherical (disk) on an axis. It's easy to understand why a top is round if we spin it. A top is round so that it can rotate and be stable.
Why does the round shape allow the top to rotate stablely? A round shape is better than any other shape because of its symmetrical mass distribution. Basically, for an object to rotate stablely it requires only one precondition ... it should have symmetrical mass distribution on its axis. If this precondition is satisfied, then the actual shape is not an important factor.
Hereafter, I define a top as an object which has symmetrical mass distribution on its axis. A top must have mass. It is irrelevant to consider mass distribution if the object doesn't have mass. If I need to identify whether a top is rotating or unrotating I will use the terms 'rotating top' and 'unrotating top'. If I simply say 'top' which is meaning 'rotating top'.
Next, let's consider what against a top doesn't tip over.
1.2 What against a top doesn't tip over
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