Most of the atoms are electrically neutral and they exchange electrons forming quantum bonding and antibonding states. This allows to form molecules with interacting atoms through the chemical bondings.
The interaction between molecules is more complex and can be due to dipole-dipole interaction, inducted dipole-dipole interaction and to what known as London forces. The London dispersion force is a temporary attractive force that results when the electrons in two adjacent atoms occupy positions that make the atoms form temporary dipoles. This force is sometimes called an induced dipole-induced dipole attraction. This force is the weakest between molecules and usually only creates liquid order or molecular solids.
The interaction in solids is a little bit more complex and it is usually classified by four bondings: molecular solids with London dispersion forces, metallic solids characterized for having delocalized electrons, ionic solids where the electrostatic interaction forms it and the covalent solids where the interaction is due to covalent bonds, i.e. sharing electrons as in the diamond which implies its so high elastic hardness.
An important addition to the various manifestations of the electromagnetic (mostly electric) forces, already mentioned, is the Fermi repulsion caused by quantum statistics. So it is actually not a classical force at all, but nevertheless very important for assuring the very existence of stable matter as we know it.
And the bosons have an attraction force due to the quantum exchange. But this interaction is mainly important for magnetic phase order in 3d and 4f electrons.
Look up van der Waals interaction (usually weak ) Somthing like a spontaneous polarization between two molecules that leads to an attraction and energy lowering.