I'll start with introducing Legendrian closures of positive braids and using them to illustrate some of the basic ideas in Legendrian knot theory. Then I'll explain how one can use this construction and a monodromy invariant (induced on the contact homology of the knot) to produce examples of S^1- families that are non-contractible in the space of Legendrian knots, even though they do contract in the space of smooth knots.