The number of detected extremely low mass (ELM) white dwarf stars has increased drastically in recent year thanks to the results of many surveys. In addition, some of these stars have been found to exhibit pulsations, making them potential targets for asteroseismology. We provide a fine and homogeneous grid of evolutionary sequences for helium (He) core white dwarfs for the whole range of their expected masses (0.15<~M_*_/M_{sun}_<~0.45), including the mass range for ELM white dwarfs (M_*_/M_{sun}_<~0.20). The grid is appropriate for mass and age determination of these stars, as well as to study their adiatabic pulsational properties. White dwarf sequences have been computed by performing full evolutionary calculations that consider the main energy sources and processes of chemical abundance changes during white dwarf evolution.