  Renormalization Group Equations (RGEs) are indispensable tool to know the
behavior of physical parameters at different energy scales. They are also
extremely crucial if we want to extend our known Standard Model gauge group by
some extra gauge groups and the $\beta$-functions are the soul of these RGEs.
In literature although it is quite common to find long, final expressions of
the RGEs, unfortunately it is difficult to find any pedagogical review to
calculate these $\beta$-function coefficients explicitly from the known
formulae. Therefore in this note we shall try to explain the detail
calculations of RGEs by giving some explicit examples taken from the
literature. The goal and hope is to provide a hand on experience on calculating
these RGEs for the young readers.
