From a physicist's point of view there are four fundamental forces: gravitational, electromagnetic, weak nuclear, and strong nuclear. The strong nuclear force keeps the quarks in hadrons (a type of subatomic particle) together. The weak force is involved in the interactions of neutrons and causes beta decay. The electromagnetic force is the interaction of charged materials or materials with a magnetic moment, and the gravitational force is the interaction between objects with mass. Note that these designations are currently debated among physicists. Physicits postulate that all four fundamental forces are essentially the same phenomena and are seeking a theoretical basis for unifying the four fundamental forces. For example, most physicists will say that the electromagnetic force and weak force are essentially the same phenomena.
Chemists (with the exception of nuclear chemists) are primarily interested in the electromagnetic force. This force is the fundamental force underlying the interaction of charged molecules, interaction of objects with moving charged (and hence magnetic moments), chemical bonding, dipole interactions, and van der Waals interactions. The electrostatic force also explains macroscopic phenomena such as friction, elastic (spring) forces, and normal forces.