Quantum numbers explain values of total conserved quantities in the dynamics of the quantum system. possibly the most peculiar part of quantum mechanics is the quantization of observable quantities, thus quantum numbers are discrete sets of integers or may be half-integers. This is distinguished from classical mechanics where the values can range continuously. Quantum numbers often illustrate specifically the energies of electrons in atoms, but other possibilities involves angular momentum, spin etc. Any quantum system may have one or more quantum numbers; thus it is difficult to list all feasible quantum numbers.
Atomic structure theory explains more about Quantum numbers.