  We present our concise notes for the lectures and tutorials on pairing,
quasi-spin and seniority delivered at SERB school on Role of Symmetries in
Nuclear Physics, AMITY University, $2019$. Starting with some generic features
of residual nucleon-nucleon interactions, we provide detailed derivation of the
matrix elements for the $\delta$-interaction which is the basis for the
standard pairing Hamiltonian. The eigen values for standard pairing Hamiltonian
are then obtained within the quasi-spin formalism. The algebra involving
quasi-spin operators is performed explicitly using the annihilation and
creation operators for single nucleon together with the application of Wicks
theorem. These techniques are expected to be helpful in deriving the mean-field
equations for the $Hartree-Fock$, $Bardeen-Cooper-Schrieffer$ and
$Hartree-Fock$ Bogoliubov theories.
