Mössbauer (nuclear γ-resonance) spectroscopy is a powerful technique that is actively used in various fields, from physics and chemistry to biology and medicine. Rudolf L. Mössbauer, who observed nuclear γ-resonance and published his results in 1958, received a Nobel Prize in physics in 1961 for this discovery. The 57Fe is the most widely used nucleus in Mössbauer spectroscopy. Therefore, a large variety of compounds containing iron can be studied by Mössbauer spectroscopy. It is well known that planetary matter contains various iron-bearing phases and minerals. Therefore, the extraterrestrial material from different meteorites, asteroids, and planets can be studied using 57Fe Mössbauer spectroscopy as additional powerful technique. Two parts of this review consider the results of more than 50 years of experience of Mössbauer spectroscopy applied for the studies of various meteorites, soils, and rocks from the Moon and recent investigation of the Mars surface using two rovers equipped with miniaturized Mössbauer spectrometers. Part I will discuss known results on Mössbauer spectroscopy of undifferentiated meteorites, which are the most primitive and formed with the solar system.