Acquaintance with the abstract algebra: semigroups

Abstract. The paper is written on the basis of the plenary report, made by the author at the All-Russian Scientific-Practical Conference “Mathematics and Computer Modeling in studies of students and pupils” (Kirov, 14-15 May 2013). The paper places accents on the process of explaining elements of Semigroup Theory to students of junior courses, studying Mathematics, and to advanced high school pupils.