  We review pedagogically non-Abelian discrete groups, which play an important
role in the particle physics. We show group-theoretical aspects for many
concrete groups, such as representations, their tensor products. We explain how
to derive, conjugacy classes, characters, representations, and tensor products
for these groups (with a finite number). We discussed them explicitly for
$S_N$, $A_N$, $T'$, $D_N$, $Q_N$, $\Sigma(2N^2)$, $\Delta(3N^2)$, $T_7$,
$\Sigma(3N^3)$ and $\Delta(6N^2)$, which have been applied for model building
in the particle physics. We also present typical flavor models by using $A_4$,
$S_4$, and $\Delta (54)$ groups. Breaking patterns of discrete groups and
decompositions of multiplets are important for applications of the non-Abelian
discrete symmetry. We discuss these breaking patterns of the non-Abelian
discrete group, which are a powerful tool for model buildings. We also review
briefly about anomalies of non-Abelian discrete symmetries by using the path
integral approach.
