There has been growing interest in the model of semiconductor lasers with non-Markovian relaxation partially due to the dissatisfaction with the conventional model for the optical gain in predicting the correct gain spectrum and the thermodynamic relations. In this book, a non-Markovian model for the optical gain of semiconductor is developed, taking into account the rigorous electronic band-structure and the non-Markovian relaxation using the quantum statistical reduced-density operator formalism. Example programs based on Fortran 77 will also be provided for band-structures of zinc-blende and wurtzite quantum wells. Many-body effects are taken into account within the time-dependent Hartree-Fock equations. Various semiconductor lasers, including the strained-layer quantum-well lasers and wurtzite GaN blue-green quantum-well lasers, will be discussed.