  The purpose of this paper is to introduce and study the notions of $f$-rack
and $f$-quandle which are obtained by twisting the usual equational identities
by a map. We provide some key constructions, examples and classification of low
order $f$-quandles. Moreover, we define modules over $f$-racks, discuss
extensions and define a cohomology complex for $f$-quandles.
