This course will offer an introduction to Loop Quantum Gravity. We will begin by exploring the challenges of quantum gravity and the motivations behind loop gravity's approach to them. Inspired by the title of this series of courses, we will work to identify a simple, finite degree of freedom, geometrical and gravitational system. This will lead us to the quantum tetrahedron, which we will then use to introduce and illustrate both the Hamiltonian approach of Loop Quantum Gravity and the discrete geometry path integrals known as spin foam models. Building up the theory with the quantum tetrahedron as a constant touchstone, I hope to emphasize the geometry of quantum gravity throughout.

Lecture 1:
- Why Quantum Gravity?
- Some of the Reasons that Quantum Gravity is Difficult
- Features of the Loop Approach to Quantum Gravity
- Overview of the Course

Below is a partial list of introductory textbooks on Loop Quantum Gravity. They vary significantly in the background assumed of the reader.
C. Rovelli, F. Vidotto: Covariant Loop Quantum Gravity, Cambridge Univ. Press, 2014.
C. Rovelli: Quantum Gravity, Cambridge Univ. Press, 2007.
J. Baez, J. P. Muniain: Gauge Fields, Knots, and Gravity, World Scientific, 1994.
R. Gambini, J. Pullin: Loop Quantum Gravity for Everyone, World Scientific, 2020.
R. Gambini, J. Pullin: A First Course in Loop Quantum Gravity, Oxford University Press, 2011.
A. Ashtekar, J. Pullin (eds.): Loop Quantum Gravity: The First 30 Years, World Scientific, 2017.
T. Thiemann: Modern Canonical Quantum General Relativity, Cambridge Univ. Press, 2007.
M. Bojowald: Quantum Cosmology - A Fundamental Description of the Universe, LNP 835, Springer, 2011.
(See also, C. Bambi, L. Modesto and I. L. Shapiro (eds.): Handbook of Quantum Gravity, Springer, expected in 2023.)