Employed in conjunction with the Aufbau principle, they are a result of spin-spin interaction, orbit-orbit interaction, and spin-orbit coupling respectively.  
The first of them can be proved exactly within the Hartree-Fock approximation.  All of them presume L-S or Russel-Saunders coupling but do not apply for heavier substances in which j-j coupling predominates.  Employed in conjunction with the Aufbau principle, they are a result of spin-spin interaction, orbit-orbit interaction, and spin-orbit coupling respectively.  The first states that the term with the maximum multiplicity lies lowest in energy and the others follow in that vein.  FTP, identify this set of guidelines that allows one to determine the quantum numbers for the ground states of atoms, a set of guidelines named for their German discoverer.
The first of them can be proved exactly within the Hartree-Fock approximation.  
Hund's rules