Carbonates, halides, native elements, oxides, silicates, sulfates, and sulfides.
Carbonate minerals contain #CO_3# (carbon and oxygen) combined with other elements. Calcite is the most common carbonate mineral.
Halides include chlorine and fluorine. Common Halides are halite (common salt) and fluorite.
Native elements are minerals that form as individual elements. Copper and gold are examples of these.
Oxides, as one can imagine, are made up of oxygen and one or more metal. Hematite is an oxide.
Silicates make up over 90% of common rock-forming minerals and contain silicon and oxygen (the two most abundant elements in the earth's crust).
Sulfates contain #SO_4# (sulfur and oxygen) combined with other elements. Gypsum is a sulfate.
Sulfides contain sulfur and metal. Common sulfide minerals are galena and pyrite.