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The paper reports on the improved Mainz experiment on tritum $\beta$spectroscopy which yields a 10 times' higher signal to background ratio thanbefore. The main experimental effects and systematic uncertainties have beeninvestigated in side experiments and possible error sources have beeneliminated. Extensive data taking took place in the years 1997 to 2001. Aresidual analysis of the data sets yields for the square of the electronantineutrino mass the final result of $m^2(\nu_e)=(-0.6 \pm 2.2_{\rm{stat}} \pm2.1_{\rm{syst}})$ eV$^2$/c$^4$. We derive an upper limit of $m(\nu_e)\leq 2.3$eV/c$^2$ at 95% confidence level for the mass itself.Comment: 22 pages, 22 figures submitted to EPJ

Final results from phase II of the Mainz neutrino mass searchin tritium ${\beta}$ decay