  We define a new algebraic structure called Legendrian racks or racks with
Legendrian structure, motivated by the front-projection Reidemeister moves for
Legendrian knots. We provide examples of Legendrian racks and use these
algebraic structures to define invariants of Legendrian knots with explicit
computational examples. We classify Legendrian structures on racks with 3 and 4
elements. We use Legendrian racks to distinguish certain Legendrian knots which
are equivalent as smooth knots.
