On constructions of semigroups

This paper gives a brief survey of constructions of semigroups by using structures of some semigroups belonging to the class of regular semigroups, quasi-regular semigroups, and abundant semigroups. In particular, we show some basic notation and structure theorems for some semigroups, for example, Rees matrix semigroups over the $0$-group $G^0$ and their generalizations, bands, $E$-ideal quasi-regular semigroups, $\mathcal C^*$-quasiregular semigroups, $\mathcal L^*$-inverse semigroups, $\mathcal Q^*$-inverse semigroups, and regular ortho-lc-monoids.