Echelle spectrophotometry of the 30 Doradus nebula in the LMC is presented. The data consist of VLT UVES observations in the 3100-10350 Angstrom range. The intensities of 366 emission lines have been measured, including 269 identified permitted lines of H-0, He-0, C-0, C+, N+, N++, O-0, O+, Ne-0, Ne+, S+, S++, Si-0, Si+, Si++, Ar+, and Mg+; many of them are produced by recombination only while others mainly by fluorescence. Electron temperatures and densities have been determined using different line intensity ratios. The He+, C++, O+, and O++ ionic abundances have been derived from recombination lines; these abundances are almost independent of the temperature structure of the nebula. Alternatively, abundances from collisionally excited lines have been derived for a large number of ions of different elements; these abundances depend strongly on the temperature structure. Accurate t(2) values have been derived from the Balmer continuum and by comparing the C++, O+, and O++ ionic abundances obtained from collisionally excited and recombination lines. The chemical composition of 30 Doradus is compared with those of Galactic and extragalactic H II regions. The values of DeltaY / DeltaO, DeltaY / DeltaZ, and Y-p are also discussed.