The 2500 or so minerals which occur in nature are classified by chemical composition and secondarily by the internal arrangement of their atoms ( crystalline structure). The following are commonly accepted classes of minerals including both elements and compounds: 

Elements They include metals such as gold (Au), silver (Ag), copper (Cu) as well as platinum (Pt) and related precious metals. They also include arsenic (As), antimony (Sb), bismuth (Bi), sulfur (S) and the two natural forms of carbon (C), diamond and graphite (which differ not in composition but in structure). 

Sulfides. In general the sulfides are a group of minerals composed of sulfur and one or more metals. For example galena (PbS) and pyrite (FeS2) are important ores of lead and iron, respectively. 

Oxides and Hydroxides. Oxides are compounds of metals and oxygen. Many of these are economically important metallic ores. Hematite (Fe2O3), magnetite (Fe3O4), and limonite (HFeO2) all belong in this class. 

Halides. This class of compounds derives its name from the fact that they include one of the elements from group VII of the periodic table (the halogens) as the main non-metal, commonly fluorine (F) and chlorine (Cl). Halite (NaCl) and fluorite (CaF2) are prime examples of this class. 

Carbonates, Nitrates, and Borates. Carbonates, by far the most common components of this class, are a combination of metal ions and CO3= . The most common carbonate mineral is calcite (CaCO3), the basic constituent of limestones. 

Sulfates. Sulfates are composed of SO4= combined with some metal. The most common sulfate is gypsum (CaS04 . 2H20). When this mineral is heated, the water is driven off and the remaining powder is called plaster of Paris. Recombining plaster with water reforms gypsum, a standard building material used in drywalls. 

Phosphates and related minerals. The minerals in this group have (P04-3) or a similar ion in their structure, again in combination with some metal. Although phosphates rarely make up large rock masses, they are a critical economic resource. Lack of phosphorus in soil is generally one of the major factors limiting plant growth, and phosphate fertilizers supply a much needed source of this element. At the present time Florida is the leading producer of phosphates in the Eastern United States. 

Silicates. Silicates (any mineral which contains silicon (Si)) are a large group which includes about one third of all minerals; and more importantly, they are the most common rock forming minerals. Over 90% of the earth's crust is made up of silicates. All silicates share a common structure of one central silicon atom linked to four oxygen atoms in a tetrahedral configuration. The various groups of silicates differ in the greater or lesser complexity of arrangement of these tetrahedra, and in the various elements which link these together. 

As mentioned above, minerals are classified on the basis of their chemistry and their structure. Yet, geology is a field science; so it is rare that a field geologist has the assistance of a well equipped chemistry lab to figure out the chemistry during field exploration. The problem then is how to recognize and identify a mineral without recourse to lab analyses.