In this and a subsequent paper, using the notion of fuzzy neighborhood filter which has been defined in [5], we introduce and study the separation axioms Ti, i = 0; 1; 2; 3; 4 in the case of a fuzzy topology. These axioms are related only to usual points and ordinary subsets. In the classical case L = f0; 1g these axioms are the usual ones. These axioms fulfills many properties analogous to the usual axioms. Whereas this paper is devoted to the axioms T0; T1; T2, in part II the axioms T3; T4 are introduced and studied. Keywords: Fuzzy filters, Principal fuzzy filters, Fuzzy neighborhood filters, Valued fuzzy neighborhoods, Fuzzy topologies, Fuzzy separation axioms