63 pages, 14 figures.-- Accepted by Eur. Phys. J. C.-- DELPHI Collaboration.A measurement of the W boson mass and width has been performed by the Delphi collaboration using the data collected during the full LEP2 programme (1996-2000). The data sample has an integrated luminosity of 660 pb−1 and was collected over a range of centre-of-mass energies from 161 to 209 GeV. Results are obtained by applying the method of direct reconstruction of the mass of the W from its decay products in both the W+W− → ℓνℓq¯q′ and W+W− → q¯q′¯qq′ channels.We acknowledge the support of Austrian Federal Ministry of Education, Science and Culture, GZ 616.364/2-III/2a/98, FNRS–FWO, Flanders Institute to encourage scientific and technological research in the industry (IWT) and Belgian Federal Office for Scientific, Technical and Cultural affairs (OSTC), Belgium, FINEP, CNPq, CAPES, FUJB and FAPERJ, Brazil, Ministry of Education of the Czech Republic, project LC527, Academy of Sciences of the Czech Republic, project AV0Z10100502, Commission of the European Communities (DG XII), Direction des Sciences de la Matière, CEA, France, Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie, Germany, General Secretariat for Research and Technology, Greece, National Science Foundation (NWO) and Foundation for Research on Matter (FOM), The Netherlands, Norwegian Research Council, State Committee for Scientific Research, Poland, SPUB-M/CERN/PO3/DZ296/2000, SPUB-M/CERN/PO3/DZ297/2000, 2P03B 104 19 and 2P03B 69 23(2002-2004), FCT - Fundaçao para a Ciência e Tecnologia, Portugal, Vedecka grantova agentura MS SR, Slovakia, Nr. 95/5195/134, Ministry of Science and Technology of the Republic of Slovenia, CICYT, Spain, AEN99-0950 and AEN99-0761, The Swedish Research Council, Particle Physics and Astronomy Research Council, UK, Department of Energy, USA, DE-FG02-01ER41155, EEC RTN contract HPRN-CT-00292-2002.Peer reviewed