ABSTRACT
8.1 Again inspired by numbers and operations with numbers, we introduce abstract binary operations on a nonempty set. Depending on the properties of this operation several new structures are defined on the set under consideration. These structures will appear in many branches of mathematics, but for our use, we view them as preparatory stages for the introduction of groups in the next Chapter. Nevertheless, let us point out that semigroups have recently founds several applications in other fields, e.g. in Computer Sciences and in Biology.
