We present new cooling sequences , color-magnitude diagrams , and color-color diagrams for cool white dwarfs with pure hydrogen atmospheres down to an effective temperature T _ { eff } = 1500 K. We include a more detailed treatment of the physics of the fully-ionized interior , particularly an improved discussion of the thermodynamics of the temperature-dependent ion-ion and ion-electron contributions of the quantum , relativistic electron-ion plasma . The present calculations also incorporate accurate boundary conditions between the degenerate core and the outermost layers as well as updated atmosphere models including the H _ { 2 } -H _ { 2 } induced-dipole absorption . We examine the differences on the cooling time of the star arising from uncertainties in the initial carbon-oxygen profile and the core-envelope L - T _ { c } relation . The maximum time delay due to crystallization-induced chemical fractionation remains substantial , from \sim 1.0 Gyr for 0.5 and 1.2 M _ { \odot } white dwarfs to \sim 1.5 Gyr for 0.6 to 0.8 M _ { \odot } white dwarfs , even with initial stratified composition profiles , and can not be ignored in detailed white dwarf cooling calculations . These cooling sequences provide theoretical support to search for or identify old disk or halo hydrogen-rich white dwarfs by characterizing their mass and age from their observational signatures . Subject headings : equation of state - stars : atmospheres - white dwarfs - Galaxy : halo