| Περίληψη: | In the first chapter a limited reference is made to the classical concept of the set as well as to algebra of the sets. The examples serve the following learning objectives: understanding importance of sets in the formation and management of data structures, categorizations and classifications of these elements, the formation of logic and pattern recognition. In the first paragraph, the evolution of the theory from Cantor to modern fuzzy set theory is briefly outlined. The detection of paradoxes played a special role in this development and the questioning of the positions originally formulated. The second, third and fourth paragraphs present the basic principles of set algebra in their classical sense. Basic relations of sets are mentioned in the fifth paragraph, while the last two paragraphs refer to fuzzy sets and the topology of fuzzy sets. Measure methods are introduced mainly with the embership functions and examples of sets of elements that are characterized by their qualitative characteristics are presented focusing on the establishment of appropriate membership function that specifies the degree of participation of the elements in the fuzzy set. More than its use as a fundamental system, set theory is a discipline of mathematics attractive to the research community. Modern research in set theory includes a diverse collection of topics, ranging from the structure of the real number line to study of the consequence for large integers.
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