Which fundamental force holds atomic nuclei together?

Atomic nuclei stay bound because the strong nuclear force is stronger than the electromagnetic repulsion between positively charged protons at nuclear distances. This force is not the same as ordinary magnetism; it is the residual effect of the color force between quarks. It acts only over about a femtometer, which is about the size of a proton. In heavier nuclei, the balance between strong attraction and proton repulsion becomes delicate, which is why some elements are unstable. Nuclear binding energy is a direct measure of this force at work.