  Consider the interior of a black hole or the very early universe: matter is
so densely localized that neither the effects of gravity nor those of quantum
theory can be ignored. But this entails that neither general relativity nor
quantum theory on its own can fully describe such a situation, for some of the
most fundamental principles inhering in these two theories are haunted by the
specter of incompatibility. Quantum gravity is the name for the bewildering
penumbra of theories that seek to exorcise this demon. But it turns out that
the metrical variables of general relativity constitute a lamp too narrow to
bottle the phantom, and loop quantum gravity is a fascinating enterprise that
seeks the Aladdin who does possess the required lamp. This is achieved by
recasting general relativity as a theory of connections, rather than that of
metrics. This shift of emphasis allows one to use a number of mathematical
tools that make it possible to arrive at a fully consistent, almost
background-independent theory of quantum gravity. This thesis endeavours to
probe these ideas in detail.
