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Theoretical femtosecond physics is a new field of research. Theoretical investigations of atoms and molecules interacting with pulsed or continuous wave lasers of up to atomic field strengths are leading to an understanding of many challenging experimental discoveries. Laser-matter interaction is treated on a nonperturbative level in the book using approximate and numerical solutions of the time-dependent Schrödinger equation. The light field is treated classically. Physical phenomena, ranging from ionization of atoms to the ionization and dissociation of molecules and the control of chemical reactions are presented and discussed. Theoretical background for experiments with strong and short laser pulses is given. Several exercises are included in the main text. Some detailed calculations are performed in the appendices.