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In this present investigation, we first give a survey of the work done so far in this area of Hankel determinant for univalent functions. Then the upper bounds of the second Hankel determinant |a2a4−a32| for functions belonging to the subclasses S(α,β), K(α,β), Ss∗(α,β), and Ks(α,β) of analytic functions are studied. Some of the results, presented in this paper, would extend the corresponding results of earlier authors.