Wikipedia has a nice list of identities for how intersections, unions, and complements interact with images and preimages of set functions.
But if $f:V \to W$ is a linear map, many of the identities for set functions can be refined. For example, if $A \subset V$, then $f^{-1}(f(A)) = A + \ker f$. There are also identities which involve sums, e.g. $f(A + B) = f(A) + f(B)$.
Can anyone point me to a reference which has a list of identities for subspaces and linear maps?