The concept of hypergeometric functions was coined by John Wallis in the middle of 17th century as a generalization of many elementary functions. Since then, these functions have played a key role in various branches of mathematics. Great mathematicians such as Euler, Gauss, Riemann and Klein have investigated the theory of hypergeometric functions from various aspects and have shown the role of these functions in the connection of differential equations, geometry and number theory. In the 20th century, with the generalizations of these functions, unexpected applications of them in theoretical physics (string theory) were found, which led to the solution of conjectures in enumerative geometry. In this lecture, we will have a general overview of these efforts.

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