  We construct equivariant and Bott-type Seiberg-Witten Floer homology and
cohomology for 3-manifolds, in particular rational homology spheres, and prove
their diffeomorphism invariance. We present several versions of the equivariant
theory: the singular version, the de Rham version and the Cartan version, with
the first playing the most important role. These versions are shown to be
equivalent to each other.
  A few typos are removed.
