Two of the most widely used classifications are those of Folk (1959,1962) and Dunham (1962). Both classifications subdivide limestones primarily on the basis of matrix content.
Most limestones are classified by Folk allochemical rocks if they contain over l0% allochems (transported carbonate grains). Based on the percentage of interstitial material, the rocks may be further subdivided into two groups: sparry allochemical limestones (containing a sparry calcite cement of clear coarsely crystalline mosaic calcite crystals) and microcrystalline allochemical limestone(containing microcrystalline calcite mud, micrite, which is subtranslucent grayish or brownish particles less than about 5 microns in size). Further subdivision is based on the allochem ratios of Folk (1962) are shown in Scholle & Ulmer-Scholle (2003).
Thus Folk's classification (figures above) is most suited for thin section study. Remember that he terms rocks with appreciable matrix as micrites while matrix-free rocks that contain sparry calcite cement are termed sparites. As you can see sparites and micrites are further subdivided by means of their most common grains.
In contrast, Dunham's classification (figures