We present high resolution large scale observations of the molecular and atomic gas in the Local Group Galaxy M33 . The observations were carried out using the HEterodyne Receiver Array ( HERA ) at the 30m IRAM telescope in the CO ( 2–1 ) line achieving a resolution of 12 \arcsec \times 2.6 { ~ { } km s ^ { -1 } } , enabling individual Giant Molecular Clouds ( GMCs ) to be resolved . The observed region is 650 square arcminutes mainly along the major axis and out to a radius of 8.5 kpc , and covers entirely the 2 \arcmin \times 40 \arcmin radial strip observed with the HIFI and PACS Spectrometers as part of the HERM33ES Herschel key program . The achieved sensitivity in main beam temperature is 20–50 mK at 2.6 ~ { } { ~ { } km s ^ { -1 } } velocity resolution . The CO ( 2–1 ) luminosity of the observed region is 1.7 \pm 0.1 \times 10 ^ { 7 } ~ { } { K { ~ { } km s ^ { -1 } } pc ^ { 2 } } and is estimated to be 2.8 \pm 0.3 \times 10 ^ { 7 } ~ { } { K { ~ { } km s ^ { -1 } } pc ^ { 2 } } for the entire galaxy , corresponding to H _ { 2 } masses of 1.9 \times 10 ^ { 8 } ~ { } { M _ { \sun } } and 3.3 \times 10 ^ { 8 } ~ { } { M _ { \sun } } respectively ( including He ) , calculated with a N ( \mathrm { H _ { 2 } } ) / \mathrm { I } _ { \mathrm { CO ( 1 - 0 ) } } twice the Galactic value due to the half-solar metallicity of M33 . H i  21 cm VLA archive observations were reduced and the mosaic was imaged and cleaned using the multi-scale task in the CASA software package , yielding a series of datacubes with resolutions ranging from 5 \arcsec to 25 \arcsec . The H i mass within a radius of 8.5 kpc is estimated to be 1.4 \times 10 ^ { 9 } { M _ { \sun } } . The azimuthally averaged CO surface brightness decreases exponentially with a scale length of 1.9 \pm 0.1  kpc whereas the atomic gas surface density is constant at \Sigma _ { { H \textsc { i } } } = 6 \pm 2 ~ { } { M _ { \sun } } pc ^ { -2 } deprojected to face-on . For a N ( \mathrm { H _ { 2 } } ) / \mathrm { I } _ { \mathrm { CO ( 1 - 0 ) } } conversion factor twice that of the Milky Way , the central kiloparsec H _ { 2 } surface density is { \Sigma _ { H _ { 2 } } = 8.5 \pm 0.2 ~ { } { M _ { \sun } } pc ^ { -2 } } . The star formation rate per unit molecular gas ( SF Efficiency , the rate of transformation of molecular gas into stars ) , as traced by the ratio of CO to H _ { \alpha } and FIR brightness , is constant with radius . The SFE , with a N ( \mathrm { H _ { 2 } } ) / \mathrm { I } _ { \mathrm { CO ( 1 - 0 ) } } factor twice galactic , appears 2–4 times greater than of large spiral galaxies . A morphological comparison of molecular and atomic gas with tracers of star formation is presented showing good agreement between these maps both in terms of peaks and holes . A few exceptions are noted . Several spectra , including those of a molecular cloud situated more than 8 kpc from the galaxy center , are presented .