TheAlgorithmicNumberTheorySymposiabeganin1994atCornellUniversity inIthaca, NewYorktorecognizethegrowingimportanceofalgorithmicwork in the theory of numbers. The subject of the conference is broadly construed toencompassadiversebodyofmathematics, andtocoverboththetheoretical andpracticaladvancesinthe?eld. Theyhavebeenheldeverytwoyearssince: inBordeaux(UniversiteBordeauxI)in1996, Portland(ReedCollege)in1998, Leiden(UniversiteitLeiden)in2000, andthepresentconferencehostedbythe MagmaComputationalAlgebraGroupattheUniversityofSydney. TheconferenceprogramincludedinvitedtalksbyManjulBhargava(Prin-...