  In this review, the fundamental structure of loop quantum gravity is
presented pedagogically. Our main aim is to help non-experts to understand the
motivations, basic structures, as well as general results. It may also be
beneficial to practitioners to gain insights from different perspectives on the
theory. We will focus on the theoretical framework itself, rather than its
applications, and do our best to write it in modern and precise langauge while
keeping the presentation accessible for beginners. After reviewing the
classical connection dynamical formalism of general relativity, as a
foundation, the construction of kinematical Ashtekar-Isham-Lewandowski
representation is introduced in the content of quantum kinematics. The
algebraic structure of quantum kinematics is also discussed. In the content of
quantum dynamics, we mainly introduce the construction of a Hamiltonian
constraint operator and the master constraint project. At last, some
applications and recent advances are outlined. It should be noted that this
strategy of quantizing gravity can also be extended to obtain other background
independent quantum gauge theories. There is no divergence within this
background independent and diffeomorphism invariant quantization programme of
matter coupled to gravity.
