Crystallography refers to the way crystals are formed.
There are six crystal systems. All minerals form crystals in one of these six systems. You may think that there are more then that, but they are all variations of one of these six systems. Each system is defined by a combination of three factors; how many axes they have, their lengths and the angles they meet. An axis is a direction between the sides.

Crystal System		Facts	Common Minerals
ISOMETRIC  Cubes  Octohedrons  Dodecahedrons  Tetrahexahedrons		The first and simplest is the isometric or cubic system. It has three axes. They are all the same length and they all intersect at 90o to each other. Because of the equality of axes, minerals in the cubic system are singly refractive. That does not apply to any other crystal system.	Copper Silver Gold Galena Halite Fluorite Garnets Sphalerite Pyrite
TETRAGONAL  Tetragonals  Tetragonal Dipyramids  Dietragonal prisms		... The tetragonal system also has three axes that all meet at 90o. It differs from the isometric system in that the C axis is longer than the A and B axis which are the same length	Rutile Apophyllite Scheelite Chalcopyrite Wulfenite Vesuvianite
HEXAGONAL  Hexagonal Prisms  Hexagonal Dipyrimids  Hexagonal pyrimid		In the hexagonal system we have an additional axes, which gives the crystals six sides. Three of these are equal in length and meet at 60o to each other. The C or vertical axis is at 90o to the shorter axes.	Beryl Apatite Quartz Graphite Mimetite Vanadinite Zincite Covellite
TRIGONAL  Trigonal Dipyrimids  Rhombohedrons  Scalenohedrons		The trigonal system is a subsystem of the hexagonal. Most gem references will list these as hexagonal.In this system all the axes are different lengths and none of them meet at 90o.	Calcite Tourmaline Dolomite Smithsonite Dioptase Hematite
ORTHORHOMBIC  Rhombic Prisms  Rhombic Dipyrimids  Rhombic Pyramids		In this system there are three axes, all of which meet at 90o to each other. However, all the axes are a different length.	Sulfer Aragonite Barite Topaz Hemimorphite Celestite Olivine
MONOCLINIC  Pinacoids		In the monoclinic system all the axes are different lengths. Two of them, the A and C axes, meet at 90o, but the third one does not.	Azurite Malachite Gypsum Micas Orthoclase Realgar Epidote
TRICLINIC		All the axes are different lengths and none of them meet at 90o	Kyanite Rhodonite Albite