We introduce xCOLD GASS , a legacy survey providing a census of molecular gas in the local Universe . Building upon the original COLD GASS survey , we present here the full sample of 532 galaxies with CO ( 1-0 ) measurements from the IRAM-30m telescope . The sample is mass-selected in the redshift interval 0.01 < z < 0.05 from SDSS , and therefore representative of the local galaxy population with M _ { \ast } > 10 ^ { 9 } M _ { \odot } . The CO ( 1-0 ) flux measurements are complemented by observations of the CO ( 2-1 ) line with both the IRAM-30m and APEX telescopes , HI observations from Arecibo , and photometry from SDSS , WISE and GALEX . Combining the IRAM and APEX data , we find that the CO ( 2-1 ) to CO ( 1-0 ) luminosity ratio for integrated measurements is r _ { 21 } = 0.79 \pm 0.03 , with no systematic variations across the sample . The CO ( 1-0 ) luminosity function is constructed and best fit with a Schechter function with parameters L _ { \mathrm { CO } } ^ { * } = ( 7.77 \pm 2.11 ) \times 10 ^ { 9 } \mathrm { K km s ^ { -1 } pc ^ { 2 } } , \phi ^ { * } = ( 9.84 \pm 5.41 ) \times 10 ^ { -4 } \mathrm { Mpc ^ { -3 } } and \alpha = -1.19 \pm 0.05 . With the sample now complete down to stellar masses of 10 ^ { 9 } M _ { \odot } , we are able to extend our study of gas scaling relations and confirm that both molecular gas fractions ( f _ { H _ { 2 } } ) and depletion timescale ( t _ { dep } ( { H _ { 2 } } ) ) vary with specific star formation rate ( or offset from the star-formation main sequence ) much more strongly than they depend on stellar mass . Comparing the xCOLD GASS results with outputs from hydrodynamic and semi-analytic models , we highlight the constraining power of cold gas scaling relations on models of galaxy formation .