Abstract: In a seminal paper (2000) Oded Schramm argued that `loop-erased' random walks on the plane under a scaling limit converge to random curves on the plane which are invariant (in law) under conformal transformations. He called these random planar curves as SLE's or Stochastic Loewner Evolutions since they satisfy a (stochastic) Lowener differential equation. Since then this rich class of curves has been rechristened as Schramm Loewner Evolutions. In this lecture, we intend to motivate and give a brief introduction to SLE's. We will look at some important properties and also mention some applications.