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Master's Thesis from the year 2017 in the subject Mathematics - Miscellaneous, grade: 10, University of Nis- Serbia (Prirodno-matematicki fakultet), language: Serbian, abstract: In this paper basic concepts of C -algebras are presented with accent on positive elements and approximate identities. After that, we investigate states of C -algebras and representations of C -algebras and prove theorems that illustrate their properties and mutual correspondences, among which are GNS construction and two Gelfand-Naimark theorems of special importance.