We present high-resolution large-scale observations of the molecular and atomic gas in the Local Group galaxy M 33. 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"x2.6km/s, 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 8.5kpc, and covers entirely the 2'x40' 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 20-50mK at 2.6km/s velocity resolution. The CO(2-1) luminosity of the observed region is 1.7+/-0.1x10^7^K.km/s.pc^2^ and is estimated to be 2.8+/-0.3x10^7^K.km/s.pc^2^ for the entire galaxy, corresponding to H_2_ masses of 1.9x10^8^ and 3.3x10^8^ respectively (including He), calculated with N(H_2_)/I_CO_(1-0) twice the Galactic value due to the half-solar metallicity of M 33. The HI 21cm 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 datacube with resolutions ranging from 5" to 25". The HI mass within a radius of 8.5kpc is estimated to be 1.4x10^9^. The azimuthally averaged CO surface brightness decreases exponentially with a scale length of 1.9+/-0.1kpc whereas the atomicgas surface density is constant at {Sigma}HI=6+/-2pc^-2^ deprojected to face-on. For an (H_2_)/I_CO_(1-0) conversion factor twice that of the Milky Way, the central kiloparsec H2 surface density is {Sigma}HI=8.5+/-0.2pc^-2^. The star formation rate per unit moecular 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 radus. The SFE, with a N(H2)/I_CO_(1-0) factor twice galactic, appears 2-4 times greater than for 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 8kpc from the galaxy center, are presented.

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