chapter 2 Requirements of the theory for the experiment -- chapter 3 Continuous spectrum and eigen-problems of resolvents -- chapter 4 Linear and bilinear functionals -- chapter 5 Definition of a quantum scattering event -- chapter 6 The adiabatic theorem and the Abel strong limit -- chapter 7 Non-stationary and stationary scattering via the strong limits -- chapter 8 Scattering matrix and transition matrix -- chapter 9 Spectral analysis of operators -- chapter 10 The existence and completeness of the Møller wave operators -- chapter 11 Four-body theories for fast ion-atom collisions -- chapter 12 Perturbation series with the correct boundary conditions -- chapter 13 The Dodd-Greider series for four-body collisions -- chapter 14 Double electron capture -- chapter 15 Simultaneous transfer and ionization -- chapter 16 Single electron detachment -- chapter 17 Single electron capture -- chapter 18 Electron capture by hydrogen-like projectiles -- chapter 19 Simultaneous Transfer and Excitation -- chapter 20 Concluding remarks and outlooks.