Levitron
The levitron, if launched properly, hangs a few centimetres above the base. Its weight is equilibrated by the forces of magnetic repulsion. The spinning top is made of a strong magnet, and three or four other magnets are hidden in the corners of the base. This is the repulsion interaction between the top, positioned above, but in the centre of the square (or triangle) formed by the magnets in the base, which keeps the levitron hanging in air.
In the picture we show a diagram of magnetic lines in the magnetic trap of the levitron. The magnets in the base have, for example, the N pole directed upwards and the top has the N pole directed downwards. The weight of the top must be chosen carefully, to place the top in the point of the equilibrium (which is determined with a quite small tolerance).
The configuration of magnets is such that the field is relatively weakest in the centre of the base. The state of a stable equilibrium (at least for a few minutes) can be obtained thanks to the rotation of the top. When the top starts to deviate from its vertical position, the precession force brings it back to the vertical position, along the magnetic lines, above the centre of the base.
It is not so easy to obtain a stable levitation. The top should spin not too fast and not too slow, its mass must be carefully chosen (some weights can be added to the top to adjust its mass). The base must be positioned horizontally. But in the end, the levitron stops spinning anyway because of the air friction forces or for other reasons.