Explain the difference between ferrite, austenite and graphite ?

Ferrite is the solid solution of carbon and other constituents in alpha-iron. It is soft, ductile and relatively weak.
Austenite is the solid solution of carbon and other constituents in gamma-iron. It exists in ordinary steels at elevated temperatures, but it is also found at ordinary temperatures in some stainless steels.
Graphite has a hexagonal layer lattice.