The force that binds atoms together to form molecules is

The electromagnetic force

Explanation:

There are four fundamental forces in nature:

- Gravitational force: it is the force that acts between any particles having mass. It is relevant only on very large scales (planets, stars), since it is the weakest of the 4 forces, so very large masses are needed in order to produce relevant effects.

- Electromagnetic force: it is the force that acts between particles with electric charge. It can be attractive or repulsive. It is the main force that acts between atoms and molecules.

- Strong nuclear force: it is the force that keeps the protons and the neutrons together inside the nucleus. It acts only on very short scales (only within the nucleus of the atom)

- Weak nuclear force: it is the force responsible for the radioactive decays of certain nuclei. It also acts on very short scales.

Therefore, the force that is responsible for binding atoms together to form molecules is the electromagnetic force.