We present Herschel SPIRE-FTS observations of Arp 220 , a nearby ultra-luminous infrared galaxy . The FTS provides continuous spectral coverage from 190 – 670 \mu m , a wavelength region that is either very difficult to observe or completely inaccessible from the ground . The spectrum provides a good measurement of the continuum and detection of several molecular and atomic species . We detect luminous CO ( J = 4-3 to 13-12 ) and water rotational transitions with comparable total luminosity \sim 2 \times 10 ^ { 8 } L _ { \odot } ; very high-J transitions of HCN ( J = 12-11 to 17-16 ) in absorption ; strong absorption features of rare species such as OH ^ { + } , H _ { 2 } O ^ { + } , and HF ; atomic lines of [ C i ] and [ N ii ] . The modeling of the continuum shows that the dust is warm , with T = 66 K , and has an unusually large optical depth , with \tau _ { \mathrm { dust } } \sim 5 at 100 \mu m. The total far-infrared luminosity of Arp 220 is L _ { \mathrm { FIR } } \sim 2 \times 10 ^ { 12 } L _ { \odot } . Non-LTE modeling of the extinction corrected CO rotational transitions shows that the spectral line energy distribution of CO is fit well by two temperature components : cold molecular gas at T \sim 50 K and warm molecular gas at T \sim 1350 ^ { +280 } _ { -100 } K ( the inferred temperatures are much lower if CO line fluxes are not corrected for dust extinction ) . These two components are not in pressure equilibrium . The mass of the warm gas is 10 % of the cold gas , but it dominates the CO luminosity . The ratio of total CO luminosity to the total FIR luminosity is L _ { \mathrm { CO } } / L _ { \mathrm { FIR } } \sim 10 ^ { -4 } ( the most luminous lines , such as J = 6-5 , have L _ { \mathrm { CO,J = 6 - 5 } } / L _ { \mathrm { FIR } } \sim 10 ^ { -5 } ) . The temperature of the warm gas is in excellent agreement with the observations of H _ { 2 } rotational lines . At 1350 K , H _ { 2 } dominates the cooling ( \sim 20 L _ { \odot } / M _ { \odot } ) in the ISM compared to CO ( \sim 0.4 L _ { \odot } / M _ { \odot } ) . We have ruled out PDR , XDR and cosmic rays as likely sources of excitation of this warm molecular gas , and found that only a non-ionizing source can heat this gas ; the mechanical energy from supernovae and stellar winds is able to satisfy the large energy budget of \sim 20 L _ { \odot } / M _ { \odot } . Analysis of the very high-J lines of HCN strongly indicates that they are solely populated by infrared pumping of photons at 14 \mu m. This mechanism requires an intense radiation field with T > 350 K . We detect a massive molecular outflow in Arp 220 from the analysis of strong P Cygni line profiles observed in OH ^ { + } , H _ { 2 } O ^ { + } , and H _ { 2 } O . The outflow has a mass \gtrsim 10 ^ { 7 } M _ { \odot } and is bound to the nuclei with velocity \lesssim 250 km s ^ { -1 } . The large column densities observed for these molecular ions strongly favor the existence of an X-ray luminous AGN ( 10 ^ { 44 } ergs s ^ { -1 } ) in Arp 220 .