1 Introduction.- 2 Quantum Theory of Gravitational-Wave Detectors.- 3 Modifying Input Optics: Double Squeezed-input.- 4 Modifying Test-Mass Dynamics: Double Optical Spring.- 5 Measuring a Conserved Quantity: Variational Quadrature Readout.- 6 MQM with Three-Mode Optomechanical Interactions.- 7 Achieving the Ground State and Enhancing Optomechanical Entanglement.- 8 Universal Entanglement Between an Oscillator and Continuous Fields.- 9 Nonlinear Optomechanical...