We present the first complete far-infrared spectrum (43-197 μm) 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, [O I] 63 and 145 μm, [O III] 52 and 88 μm , [N II] 122 μm, [N III] 57 μm, and [C II] 158 μm, and fitted their ratios to a combination starburst and photodissociation region (PDR) model. The best fit is obtained with H II regions with n = 250 cm-3, an ionization parameter of 10-3.5, and PDRs with n = 103.3 cm-3 and a far-ultraviolet flux of G0 = 102.8. 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⊙ cutoff. We also detected the ground-state rotational line of OH in absorption at 119.4 μm. No excited level OH transitions are apparent, indicating that the OH is almost entirely in its ground state with a column density ∼4 × 1014 cm-2. The spectral energy distribution over the long-wavelength spectrometer wavelength range is well fitted with a 48 K dust temperature and an optical depth, τDust ∝ λ-1.