Introduction -- In the Beginning -- The Enigma of Edith: Free Energy, Nucleation and the Formation of Mineral -- Form and Function of Tissues that Undergo Mineralization -- Genes and Gene Networks Regulating Mineralization -- Calcium and Phosphate Ion Uptake, Distribution and Homeostasis in Cells of Vertebrate Mineralizing Tissues -- Calcium and Phosphate Ion Efflux from Cells: The Roles of Matrix Vesicles, Extracellular Vesicles, and Other Membrane-invested Transporters in Vertebrate Hard Tissue Mineralization -- Collagen-based Mineralization of Bones, Teeth and Other Vertebrate Skeletal Tissues -- The Role of Non-collagenous Proteins and Other Matrix Molecules in Vertebrate Mineralization -- Local and Systemic Regulation of Mineralization: Role of Coupling Factors, Pyrophosphate, Polyphosphates, Vitamin D, Fetuin, Matrix Gla Protein and Osteopontin -- Observations Concerning Mineral Deposition in Soft Tissues: Regulation of Aberrant Mineral Deposits -- Epilogue.