  The purpose of these lectures is to discuss in some detail a new,
non-perturbative approach to quantum gravity. I would like to present the basic
ideas, outline the key results that have been obtained so far and indicate
where we are headed and what the hopes are. The audience at this summer school
had a diverse background; many came from high energy physics, some from
mathematical physics and the rest from general relativity. Therefore, I have
tried to keep the technicalities --particularly proofs and even the number of
equations-- to a minimum. My hope is that a research student in any of these
three fields should be able to get a bird's eye view of the entire program. In
particular, I have kept all three perspectives in mind while discussing the
difficulties one encounters and strategies one adopts and in evaluating the
successes and limitations of the program.
