A sunspot EUV spectrum covering the wavelength range from 1175 to 1714 A with high spatial and spectral resolution is examined which contains about 200 lines not previously reported in solar spectra. Many of the lines are identified as transitions in the Lyman bands of H2. It is shown that the H2 lines are photoexcited not only by H L-alpha, as reported previously, but also by the strong transition-region lines of C II, Si IV, and O IV. The line intensities are analyzed as far as is possible at present, and differences between the quiet chromosphere and the sunspot chromosphere are deduced. The polarization of the observed lines is briefly discussed, the importance of the H L-alpha fluorescence mechanism for the excitation of the H2 Lyman bands is demonstrated, and it is concluded that the H2 lines could also be observable in stars of spectral type later than the sun.