  This article sketches various ideas in contact geometry that have become
useful in low-dimensional topology. Specifically we (1) outline the proof of
Eliashberg and Thurston's results concerning perturbations of foliatoins into
contact structures, (2) discuss Eliashberg and Weinstein's symplectic handle
attachments, and (3) briefly discuss Giroux's insights into open book
decompositions and contact geometry. Bringing these pieces together we discuss
the construction of ``symplectic caps'' which are a key tool in the application
of contact/symplectic geometry to low-dimensional topology.
