  According to the Auslander's formula one way of studying an abelian category
${\mathcal{C}}$ is to study ${\rm mod}\mbox{-}{\mathcal{C}}$, that has nicer
homological properties than ${\mathcal{C}}$, and then translate the results
back to ${\mathcal{C}}$. Recently Krause gave a derived version of this formula
and thus renewed the subject. This paper contains a detailed study of various
versions of Auslander formula including the versions for all modules and for
unbounded derived categories. We apply them to include some results concerning
recollements of triangulated categories.
