The Road to Reality by Roger Penrose in 2004
13. Symmetry groups
14. Calculus on manifolds
15. Fibre bundles and gauge connections
15.1 Some physical motivations for fibre bundles
15.2 The mathematical idea of a bundle
15.3 Cross-sections of bundles
15.4 The Clifford bundle
15.5 Complex vector bundles, (co)tangent bundles
15.6 Projective spaces
15.7 Non-triviality in a bundle connection
15.8 Bundle curvature
16. The ladder of infinity
17. Spacetime
18. Minkowskian geometry
19. The classical fields of Maxwell and Einstein
20. Lagrangians and Hamiltonians
21. The quantum principle
22. Quantum algebra, geometry, and spin
23. The entangled quantum world
24. Dirac’s electron and antiparticles
25. The standard model of particle physics
26. Quantum field theory
27. The big bang and its thermodynamic legacy
28. Speculative theories of the early universe
29. The measurement paradox
30. Gravity’s role in quantum state reduction
31. Supersymmetry, supra-dimensionality, and strings
32. Einstein’s narrower path; loop variables
33. More radical perspectives; twistor theory
34. Where lies the road to reality