Faltings' theorem states that an algebraic curve of genus at least 2 over a number field has only finitely many rational points. This striking result demonstrates how geometry can influence arithmetic properties. In this talk, I will present Bombieri's simplification of Vojta's proof. The key idea is to embed the curve into its Jacobian and study the height pairing on it. We will employ techniques from diophantine approximation to prove Vojta's inequality, which imposes a stringent condition on rational points.