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Abstract: Hopf-Galois theory is a generalization of the classical Galois theory. The concept of Hopf-Galois extension is due to Chase and Sweedler [1]. They introduced it in 1969 to study purely inseparable extensions of fields and ramified extensions of rings. Then, in 1987, Greither and Pareigis [2] developed Hopf-Galois theory for separable field extensions. In the first part of this talk, we will present Hopf-Galois structures of separable field extensions by going from well known results within Galois theory. Then we will focus on Hopf-Galois structures which are minimal. All along the talk, we will give detailed examples.