•A petrological classification is proposed adapting Earth classifications to Mars.•The classification involves the characterization of texture and chemistry.•The classification highlights the various categories of rocks analyzed by Curiosity.•Composition of in-place sedimentary rocks contrasts with that of igneous float rocks. Rocks analyzed by the Curiosity rover in Gale crater include a variety of clastic sedimentary rocks and igneous float rocks transported by fluvial and impact processes. To facilitate the discussion of the range of lithologies, we present in this article a petrological classification framework adapting terrestrial classification schemes to Mars compositions (such as Fe abundances typically higher than for comparable lithologies on Earth), to specific Curiosity observations (such as common alkali-rich rocks), and to the capabilities of the rover instruments. Mineralogy was acquired only locally for a few drilled rocks, and so it does not suffice as a systematic classification tool, in contrast to classical terrestrial rock classification. The core of this classification involves (1) the characterization of rock texture as sedimentary, igneous or undefined according to grain/crystal sizes and shapes using imaging from the ChemCam Remote Micro-Imager (RMI), Mars Hand Lens Imager (MAHLI) and Mastcam instruments, and (2) the assignment of geochemical modifiers based on the abundances of Fe, Si, alkali, and S determined by the Alpha Particle X-ray Spectrometer (APXS) and ChemCam instruments. The aims are to help understand Gale crater geology by highlighting the various categories of rocks analyzed by the rover. Several implications are proposed from the cross-comparisons of rocks of various texture and composition, for instance between in place outcrops and float rocks. All outcrops analyzed by the rover are sedimentary; no igneous outcrops have been observed. However, some igneous rocks are clasts in conglomerates, suggesting that part of them are derived from the crater rim. The compositions of in-place sedimentary rocks contrast significantly with the compositions of igneous float rocks. While some of the differences between sedimentary rocks and igneous floats may be related to physical sorting and diagenesis of the sediments, some of the sedimentary rocks (e.g., potassic rocks) cannot be paired with any igneous rocks analyzed so far. In contrast, many float rocks, which cannot be classified from their poorly defined texture, plot on chemistry diagrams close to float rocks defined as igneous from their textures, potentially constraining their nature.