Noncommutative geometry is a new field that is among the great challenges of present-day mathematics. Its methods allow one to treat noncommutative algebras - such as algebras of pseudodifferential operators, group algebras, or algebras arising from quantum field theory - on the same footing as commutative algebras, that is, as spaces. The applications range over many fields of mathematics and mathematical physics. This volume contains the proceedings of the workshop on 'Cyclic Cohomology and Noncommutative Geometry' held at The Fields Institute (Waterloo, ON) in June 1995. The workshop was part of the program for the special year on operator algebras and its applications. It features: contributions by originators of the subject who are leaders in the field; survey articles not previously available; and expository articles geared toward the larger mathematical community.