So, you want to do Quantum Gravity?

As the name suggests, working in Quantum Gravity requires a good understanding of both 'Quantum' and 'Gravity'. Here, I have tried to provide a step-by-step list of resources and readings to help you get started in this field. Other excellent (and much more detailed) resources include:

• So you want to learn Physics - Susan Rigetti
  (An excellent guide on how and where to learn physics)

• How to become a good theoretical physicist - t'Hooft
  (An excellent resource with lots of details, recommended textbooks, and links to lecture notes)

I expect any students interested in working with me to have completed (with good standing) the 4 steps listed below:

1. A solid high-school level education (FSc/A-levels/IB etc.) with strong foundations in Mathematics and Physics.

2. Calculus-I (Differentiation, Integration, Differential equations)
   Calculus-II (Multivariable calculus)
   Mechanics-I (Newton's laws, kinematics, dynamics, rotational motion, simple harmonic motion, waves and oscillations, Newtonian gravitation)
   Modern Physics (Special relativity, Quantum physics).

3. Linear Algebra (Vector spaces, transformations)
   Mathematical Methods-I (ODEs, PDEs, Fourier transform)
   Mechanics-II (Lagrangian, Hamiltonian formulations, Phase space, classical field theory)
   Quantum Mechanics-I (Hilbert spaces, 1D problems, simple harmonic oscillator)
   Quantum Mechanics-II (3D problems, Spin, Hydrogen atom, Perturbation theory)
   Quantum Mechanics-III (Path integrals, density matrix formulation, Interpretations, Dirac equation).

4. Mathematical Methods-II (Complex analysis, tensors, group theory)
   Differential Geometry (First, Second fundamental forms, curvature, Gauss-Codazzi equations, Gauss' Theorem)
   General Relativity (Manifolds, curvature, Einstein equations, Spherical symmetry, cosmology)
   Quantum Field Theory (Scalar fields, Feynman diagrams, renormalization).

Beyond these foundations, readings will vary depending on the exact program in Quantum Gravity, and personal preferences. Here are mine (primarily in canonical quantum gravity):

• Hamiltonian formulation of General Relativity

• History of Quantum Gravity - Rovelli

• Prima Facie Questions in Quantum Gravity - Isham

• Structural Issues in Quantum Gravity - Isham

• Canonical Quantum Gravity and the Problem of Time - Isham

• String Theory vs Loop Quantum Gravity? - Rovelli

Some other useful links:

• How to give a talk? - Geroch

• A Physics book list

• Another Physics book list (theoretical)

• A Math book list

• List of Resources on HEP

• Topics in Theoretical Physics - Bombelli
  (An enormous resource of brief notes and references in theoretical physics - including on quantum gravity)

• The Net Advance of Physics
  (link to general relativity)