An Invitation to String Theory
  It is hoped that these lectures will give a point of entry into that vast web of related ideas that go under the name "string theory". I start with a more or less qualitative introduction to gravity as a field theory and sketch how one might try to quantize it. Quantizing gravity using the usual techniques of field theory will turn out to be unsuccessful, and that will be a motivation for trying an indirect approach: string theory. I present bosonic string theory, quantize the closed string in the light cone gauge and show that one of the states in the closed string Hilbert space can be interpreted as a graviton. I will end with some general qualitative ideas on slightly more advanced topics. 
Chethan Krishnan