| 1 | | Setting the stage | | 1 |
| 2 | | Linear algebra over the complex numbers | | 41 |
| 3 | | Complex scalar product spaces (a.k.a. Hilbert spaces) | | 77 |
| 4 | | Lie groups and Lie group representations | | 111 |
| 5 | | New representations from old | | 153 |
| 6 | | Irreducible representations and invariant integration | | 179 |
| 7 | | Representations and the hydrogen atom | | 209 |
| 8 | | The algebra so(4) symmetry of the hydrogen atom | | 229 |
| 9 | | The group SO(4) symmetry of the hydrogen atom | | 283 |
| 10 | | Projective representations and spin | | 299 |
| 11 | | Independent events and tensor products | | 339 |