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 30 m IRAM telescope in the CO(2-1) line, achieving a resolution of 12 × 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 × 40 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 ± 0.1 × 10 7 K km s −1 pc 2 and is estimated to be 2.8 ± 0.3 × 10 7 K km s −1 pc 2 for the entire galaxy, corresponding to H 2 masses of 1.9 × 10 8 M and 3.3 × 10 8 M 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 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 to 25 . The H i mass within a radius of 8.5 kpc is estimated to be 1.4 × 10 9 M . The azimuthally averaged CO surface brightness decreases exponentially with a scale length of 1.9 ± 0.1 kpc whereas the atomic gas surface density is constant at Σ H i = 6± 2 M pc −2 deprojected to face-on. For an N(H 2 )/I CO(1−0) conversion factor twice that of the Milky Way, the central kiloparsec H 2 surface density is Σ H 2 = 8.5 ± 0.2 M 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 α and FIR brightness, is constant with radius. The SFE, with a N(H 2 )/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 8 kpc from the galaxy center, are presented.