This volume contains the proceedings of the Third Edoardo Amaldi Conference on Gravitational Waves. The Amaldi Conference had been held twice before, in Frascati, Italy (1994), and at CERN, Geneva, Switzerland (1997), but took on a new significance after it was designated the cornerstone meeting for the recently formed Gravitational Wave International Committee (GWIC). How to detect gravitational waves is the subject of the Amaldi Conference. Their detection would open a new way of doing astrophysics, different from observing electromagnetic radiation or detecting neutrinos. The proceedings describe the status of both the newest interferometers (land-based and space-based) and bar antennae that will be built to detect gravitational waves. The latest lasers, optics, and suspensions are discussed, as well as advances in signal processing and data analysis.