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 G0 and their generalizations, bands, E-ideal quasi-regular semigroups, cal C*-quasiregular semigroups, cal L*-inverse semigroups, cal Q*-inverse semigroups, and regular ortho-lc-monoids.