Abstract : Most people are familiar with Fermat's last theorem and aware that it has been proved (by Andrew Wiles). But not many know about Falting's theorem which implies the following: for $n > 4$, the equation $x^n + y^n = z^n$ has only finitely many integral solutions for which $(x,y,z)$ have no proper common factor other than $1$. Faltings's theorem is a finiteness assertion about integral zeroes of a homogeneous polynomial $P(x,y,z)$ in $3$ variables - the finiteness holds if the set of complex zeroes (in $\C^3$) satisfies a geometric condition. In this talk I will explain the statement of the theorem elaborating on the geometric concepts needed.