There are four types of quantum numbers that specify the location and energy of an electron in an atom: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (s). The principal quantum number represents the main energy level of an electron. The azimuthal quantum number corresponds to electron subshells like s, p, d, and f. The magnetic quantum number specifies the spatial orientation of an electron, and the spin quantum number indicates the electron's spin direction.