1. Introduction.- 2. Linear operators.- 3. The wave equation.- 4. The spectrum of A and boundary value problems.- 5. The free space problem for the wave equation.- 6. The wave equation continued: time-asymptotic behaviour of the solutions.- 7. Linear acoustics.- 8. Maxwell’s equations.- 9. Linear acoustics and Maxwell’s equations continued.- 10. A Schrödinger equation.- 11. Linear elasticity.- 12. The plate equation.- 13. Linear thermoelasticity.- A.1 Proof of Theorem 5.6.- A.2 Proof of Korn’s inequality.- References.- Notation.