What are the different types of igneous rock?

There are two types of igneous rock. The first type is intrusive, otherwise known as plutonic, and the second type is extrusive, otherwise known as volcanic.
Intrusive igneous rocks are formed when the magma from a volcano cools down beneath the crust of the earth. Intrusive igneous rocks are very hard and have a very rough texture. Granite is a good example of an intrusive igneous rock.
Extrusive rocks, on the other hand, are formed when the the magma from a volcano cools down above the crust of the earth, on the earth's surface. Magma that cools on the earth's surface cools more quickly than does magma beneath the earth's crust, and this slower cooling results in smoother, more fine-grained rocks. Basalt is a good example of an extrusive igneous rock.