The Third International Workshop on Numerical Analysis and Lattice QCD tookplaceattheUniversityofEdinburgh fromJune30th toJuly4th,2003. It continued a sequence which started in 1995 at the University of Kentucky and continuedin1999withaworkshopattheUniversityofWuppertal.Theaimof these workshops is to bring together applied mathematicians and theoretical physicists to stimulate the exchange of ideas between leading experts in the ?elds of lattice QCD and numerical analysis. Indeed, the last ten years have seen quite a substantial increase in cooperation between the two scienti?c communities, and particularly so between numerical linear algebra and lattice QCD. The workshop was organised jointly by the University of Edinburgh and the UK National e-Science Centre. It promoted scienti?c progress in lattice QCD as an e-Science activity that encourages close collaboration between the core sciences of physics, mathematics, and computer science. In order to achieve more realistic computations in lattice quantum ?eld theory substantial progress is required in the exploitation of numerical me- ods.Recently, therehasbeenmuchprogressintheformulationoflatticechiral symmetry satisfying the Ginsparg Wilson relation. Methods for impleme- ing such chiral fermions e?ciently were the principal subject of this meeting, which, in addition, featured several tutorial talks aiming at introducing the important concepts of one ?eld to colleagues from the other. These proce- ings re?ect this, being organised in three parts: part I contains introductory surveypapers, whereaspartsIIandIIIcontainlatestresearchresultsinlattice QCD and in computational methods."