  The paper deals with topologically trivial Legendrian knots in tight and
overtwisted contact 3-manifolds. The first part contains a thorough exposition
of the proof of the classification of topologically trivial Legendrian knots
(i.e. Legendrian knots bounding embedded 2-disks) in tight contact 3-manifolds.
This part was essentially written more than 10 years ago, but only a short
version, without the detailed proofs, was published (in CRM Proc. Lecture
Notes, Vol. 15, 1998). That paper also briefly discussed the overtwisted case.
  The final part of the present paper contains a more systematic discussion of
Legendrian knots in overtwisted contact manifolds, and in particular, gives the
coarse classification (i.e. classification up to a global contactomorphism) of
topologically trivial Legendrian knots in overtwisted contact S^3.
