Title: Representation of integers by binary forms.

Abstract: Let F (x, y) be an irreducible binary form with integral coefficients. If the degree of F is greater than 2 then by a well-known result of Thue, the equation F(x,y) = m (m an integer) has only finitely many solutions in integers x and y. I shall discuss some methods from Diophantine analysis and geometry of numbers to obtain upper bounds upon the number of integral solutions to such equations. Then I will show some results on representation of integers by binary forms with a specific emphasis on the important case of cubic equations.