  We present a pedagogical introduction to the notions underlying the
connection formulation of General Relativity - Loop Quantum Gravity (LQG) -
with an emphasis on the physical aspects of the framework. We begin by
reviewing General Relativity and Quantum Field Theory, to emphasise the
similarities between them which establish a foundation upon which to build a
theory of quantum gravity. We then explain, in a concise and clear manner, the
steps leading from the Einstein-Hilbert action for gravity to the construction
of the quantum states of geometry, known as \emph{spin-networks}, which provide
the basis for the kinematical Hilbert space of quantum general relativity.
Along the way we introduce the various associated concepts of \emph{tetrads},
\emph{spin-connection} and \emph{holonomies} which are a pre-requisite for
understanding the LQG formalism. Having provided a minimal introduction to the
LQG framework, we discuss its applications to the problems of black hole
entropy and of quantum cosmology. A list of the most common criticisms of LQG
is presented, which are then tackled one by one in order to convince the reader
of the physical viability of the theory.
  An extensive set of appendices provide accessible introductions to several
key notions such as the \emph{Peter-Weyl theorem}, \emph{duality} of
differential forms and \emph{Regge calculus}, among others. The presentation is
aimed at graduate students and researchers who have some familiarity with the
tools of quantum mechanics and field theory and/or General Relativity, but are
intimidated by the seeming technical prowess required to browse through the
existing LQG literature. Our hope is to make the formalism appear a little less
bewildering to the un-initiated and to help lower the barrier for entry into
the field.
