The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the article should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the article is essentially selfcontained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the article to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.

Applications of Riemannian quantum geometry to cosmology have had notable successes. In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big bang singularity. However, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has not been made explicit. The purpose of this paper is to address these issues, thereby providing a rmer mathematical and conceptual foundation to the subject.