part Part I: Cold Collisions -- chapter 1 Theory of Cold Atomic and Molecular Collisions / chapter 2 Electric Dipoles at Ultralow Temperatures / chapter 3 Inelastic Collisions and Chemical Reactions of Molecules at Ultracold Temperatures / chapter 4 Effects of External Electromagnetic Fields on Collisions of Molecules at Low Temperatures / part Part II: Photoassociation -- chapter 5 Ultracold Molecule Formation by Photoassociation / chapter 6 Molecular States Near a Collision Threshold / chapter 7 Prospects for Control of Ultracold Molecule Formation via Photoassociation with Chirped Laser Pulses / chapter 8 Adiabatic Raman Photoassociation with Shaped Laser Pulses / part Part III: Few- and Many-Body Physics -- chapter 9 Ultracold Feshbach Molecules / chapter 10 Molecular Regimes in Ultracold Fermi Gases / chapter 11 Theory of Ultracold Feshbach Molecules / chapter 12 Condensed Matter Physics with Cold Polar Molecules / part Part IV: Cooling and Trapping -- chapter 13 Cooling, Trap Loading, and Beam Production Using a Cryogenic Helium Buffer Gas / chapter 14 Slowing, Trapping, and Storing of Polar Molecules by Means of Electric Fields / part Part V: Tests of Fundamental Laws -- chapter 15 Preparation and Manipulation of Molecules for Fundamental Physics Tests / chapter 16 Variation of Fundamental Constants as Revealed by Molecules: Astrophysical Observations and Laboratory Experiments / part Part VI: Quantum Computing -- chapter 17 Quantum Information Processing with Ultracold Polar Molecules / part Part VII: Cold Molecular Ions -- chapter 18 Sympathetically Cooled Molecular Ions: From Principles to First Applications