Abstract: In string theory, one ends up looking at enumerative geometry of counting algebraic (over complex numbers) curves with constraints in Calabi-Yau varieties. In this talk however, we will start from the most simplest case of looking at the theory in projective spaces. I will start with discussion with the brief motivation, then set up Kontsevich moduli space of stable maps. Then we will explore GW-invariants and quantum cohomology, then see how these methods from physics give systematic answer to finding number of plane curves passing through aome number of points. If time is left, I will explain why situation gets complicated in Calabi-Yau case.