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Canonical quantum gravity was first developed by Abhay Ashtekar, Lee Smolin,Carlo Rovelli and their collaborators in the late 1980s. It was a majorbreakthrough that successfully brought Einstein's theory of General Relativity(GR) into a Yang-Mills-type gauge theory. A new era of quantum gravity researchhas since started, and with decades of continued efforts from a relativelysmall community, the area now known as Loop Quantum Gravity (LQG) hasflourished, making it a promising theory of quantum gravity. Due to itsincredibly high level of complexity, many technical details were left out inintroductory texts on LQG. In particular, resources that are appropriate to theundergraduate level are extremely limited. Consequently, there exists a hugegap between the knowledge base of an undergraduate physics major and thenecessary readiness to carry out LQG research. In an effort to fill this gap,we aim to develop a pedagogical user guide that provides a step-by-stepwalk-through of canonical quantum gravity, without compromising necessarytechnical details. We hope that our attempt will bring more exposure toundergraduates on the exciting early developments of canonical quantum gravity,and provide them with the necessary foundation to explore active researchfields such as black hole thermodynamics, Wheeler-DeWitt equation, and so on.This work will also serve as a solid base for anyone hoping to pursue furtherstudy in LQG at a higher level.

Step-by-Step Canonical Quantum Gravity -- Part I: Ashtekar's New Variables