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Number field is one of the main objects in number theory. In this talk, our aim is to give a brief introduction to number fields as one may guess from the title. First, we will define what a field extension is and then focus on algebraic extensions. In the second part of the talk, we will define number field and introduce some basic concepts such as the discriminant of any basis of a number field, norm and trace. If time permits, we will also present algebraic integers and the ring of integers of a number field. This talk is mainly designed for undergraduate students, so basic knowledge about linear algebra is sufficed.