We present the first complete far-infrared spectrum (43 to 197 um) of M82, the brightest infrared galaxy in the sky, taken with the Long Wavelength Spectrometer of the Infrared Space Observatory (ISO). We detected seven fine structure emission lines, [OI] 63 and 145 um, [OIII] 52 and 88 um, [NII] 122 um, [NIII] 57 um and [CII] 158 um, and fit their ratios to a combination starburst and photo-dissociation region (PDR) model. The best fit is obtained with HII regions with n = 250 cm^{-3} and an ionization parameter of 10^{-3.5} and PDRs with n = 10^{3.3} cm^{-3} and a far-ultraviolet flux of G_o = 10^{2.8}. We applied both continuous and instantaneous starburst models, with our best fit being a 3-5 Myr old instantaneous burst model with a 100 M_o cut-off. We also detected the ground state rotational line of OH in absorption at 119.4 um. No excited level OH transitions are apparent, indicating that the OH is almost entirely in its ground state with a column density ~ 4x10^{14} cm^{-2}. The spectral energy distribution over the LWS wavelength range is well fit with a 48 K dust temperature and an optical depth, tau_{Dust} proportional to lambda^{-1}.
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