We report novel methods for the chemical purification of Mg from silicate rocks by ion-exchange chromatography, and high-precision analysis of Mg-isotopes by high-resolution multiple collector inductively coupled plasma source mass spectrometry (HR-MC-ICPMS). Using these methods, we have measured the relative and absolute Mg-isotope composition of a number of terrestrial and extraterrestrial materials, including international reference rock standards as well as pure Mg standards, olivine crystals separated from a mantle-derived spinel lherzolite (J12 olivine), one enstatite chondrite, a martian shergottite and sea water samples. Repeated analyses of terrestrial and extraterrestrial samples demonstrate that it is possible to routinely measure the relative Mg-isotope composition of silicate materials with an external reproducibility of 2.5 and 20 ppm for the μ26Mg* and μ25Mg values, respectively (μ notation is the per 106 deviation from a reference material). Analyses of bulk mantle-derived rocks as well as a martian shergottite and an enstatite chondrite define a restricted range in μ25Mg of −120 ± 28 ppm (2sd) relative to the DSM-3 reference standard (μ25,26Mg = 0), suggesting that the Mg-isotope composition of inner solar system bulk planetary materials is uniform within the resolution of our analyses. We have determined the absolute Mg-isotope composition of the J12 olivine, two CI chondrites as well as the DSM-3 and Cambridge-1 reference standards using a mixed 26Mg-24Mg double-spike. The differences between the absolute 25Mg/24Mg ratios of the various materials analyzed relative to the DSM-3 standard are in excellent agreement with results obtained by the sample-standard bracketing method. Based on the averages obtained for the J12 olivine separates, we estimate the absolute Mg-isotope composition for Earth's mantle – and hence that of the bulk silicate Earth – to be 25Mg/24Mg = 0.126896 ± 0.000025 and 26Mg/24Mg = 0.139652 ± 0.000033. Given the restricted range of μ25Mg obtained for bulk planetary material by the sample-standard bracketing technique and the excellent agreement between the data obtained by the relative and absolute methods, we propose that these new values represent the absolute Mg-isotope composition of the bulk inner solar system. Using the absolute Mg-isotope composition of the J12 olivine, we calculate the isotopic abundances of Mg as 24Mg = 0.789548 ± 0.000026, 25Mg = 0.100190 ± 0.000018, and 26Mg = 0.110261 ± 0.000023. Based on this result, we have calculated an atomic weight for Mg of 24.305565 ± 0.000045, which is marginally heavier than previous estimates but a factor of 10 more precise.