What are the 3 classifacations of igneous rocks?

Answer 1

There are two
INTRUSIVE
the magma cooled of slowly, leaving gross crystals (granit)
EXTRUSIVE
the magma cooled off fast, leaving crystal so small you can't see them (basalt)

Answer 2

This should help. http://en.wikipedia.org/wiki/Igneous_rock#Classification

[edit] Mineralogical classification
For volcanic rocks, mineralogy is important in classifying and naming lavas. The most important criteria is the phenocryst species, followed by the groundmass mineralogy. Often, where the groundmass is aphanitic, chemical classification must be used to properly identify a volcanic rock.

Mineralogic contents - felsic versus mafic

felsic rock, with predominance of quartz, alkali feldspar and/or feldspathoids: the felsic minerals; these rocks (e.g., granite) are usually light coloured, and have low density.
mafic rock, with predominance of mafic minerals pyroxenes, olivines and calcic plagioclase; these rocks (example, basalt) are usually dark coloured, and have higher density than felsic rocks.
ultramafic rock, with more than 90% of mafic minerals (e.g., dunite)
For intrusive, plutonic and usually phaneritic igneous rocks where all minerals are visible at least via microscope, the mineralogy is used to classify the rock. This usually occurs on ternary diagrams, where the relative proportions of three minerals are used to classify the rock.

The following table is a simple subdivision of igneous rocks according both to their composition and mode of occurrence.

Composition
Mode of occurrence Acid Intermediate Basic Ultrabasic
Intrusive Granite Diorite Gabbro Peridotite
Extrusive Rhyolite Andesite Basalt Komatiite