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Well, there are basically two things that hold it together. Two forces, that is. The first of these has to do with electric charge, Electric charge comes in two varieties: positive and negative. The main carriers of positive charge are protons, while the main carriers of negative charge are electrons. (Within protons and neutrons, the quarks themselves carry charge, but this is only important to us in that the net charge of a proton or neutron is equal to the sum of the charges of all its quarks: zero for a neutron, and a small positive amount for a proton.) Every proton carries exactly the same amount of positive charge, and every electron carries a negative charge exactly opposite that of a proton. There are other particles with electric charge, but they tend to live only a very short time before they decay, and so they're mostly unimportant for atoms.
The Bond Mechanism is the actual force that holds bonded atoms together once they are joined
Some type of electric force is what holds atoms together. The nucleus of an atom is held together by nuclear binding energy, but the whole of the atom, it's "concentrated" positive charge as bound into the nucleus and the electron cloud around it, are a direct result of the dynamic action of electromagnetic forces.