  We give explicit equations that describe the character variety of the figure
eight knot for the groups SL(3,C), GL(3,C) and PGL(3,C). This has five
components of dimension 2, one consisting of totally reducible representations,
another one consisting of partially reducible representations, and three
components of irreducible representations. Of these, one is distinguished as it
contains the curve of irreducible representations coming from $Sym^2:SL(2,C)
\to SL(3,C)$. The other two components are induced by exceptional Dehn fillings
of the figure eight knot. We also describe the action of the symmetry group of
the figure eight knot on the character varieties.
