Introduction to Loop Quantum Gravity: Rovelli's lectures on LQG

These notes are a transcript of Carlo Rovelli's lectures on Loop Quantum Gravity, given in Marseille in 2018, which (at present) can be entirely found on YouTube. I transcribed them in LaTeX in early 2020 as an exercise to get ready for my Ph.D. in LQG at Western University. This transcript is meant to be a (hopefully helpful) integration for the video version. I reported the order of the topics and the chronological structure exactly as presented by Rovelli throughout the course, primarily to facilitate the comparison. Each Section corresponds to a different Lecture. The parts written in textit are my additions. Sometimes in the text, I report references, which specify precisely the minute and the second of the corresponding video on YouTube, to very short historical digressions or excursus made during the lectures by Rovelli that I have not explicitly transcribed in these notes. Where appropriate, I took some figures from the book "Covariant Loop Quantum Gravity - An elementary introduction to Quantum Gravity and Spinfoam Theory" by Carlo Rovelli and Francesca Vidotto, to which I always refer by the term "the book" in the following. For what concerns the equations, where possible, I tried to write down the "correct" versions present within the book. Finally, I thank Carlo Rovelli himself for reviewing these notes. I apologize in advance for any errors, and I wish everyone a lot of fun!