The dual UV/IR spectrometer SPICAM on board the European mission Mars Express is dedicated to monitoring the Martian atmosphere and has recorded spectra for more than one Martian year, from January 2004 to April 2006, over a large range of latitudes and longitudes. SPICAM UV spectra were recorded on the day side in a nadir geometry, in the 110--320 nm range, allowing measurement of ozone absorption around 250 nm. The method used to retrieve column-integrated ozone quantities is described. A full radiative transfer forward model of the radiance factor is used in an iterative loop to fit the data with four parameters: the surface albedo at 210 and 300 nm, the dust opacity, and the total ozone column. The analysis of the complete data set is presented. The global climatology of ozone on Mars is retrieved for the first time with spatial and temporal coverage. The most significant findings are (1) large increases in the ozone column density at high latitudes during late winter-early spring of each hemisphere that totally disappear during summer, (2) a large variability of the northern spring content related to the polar vortex oscillations, (3) low ozone columns in the equatorial regions all year long, and (4) local variations of the ozone column related to topography, mainly above Hellas Planitia. A good overall agreement is obtained comparing SPICAM data to predictions of a Chemical General Circulation Model. However, significant discrepancies in total abundances are found near northern spring when ozone reaches its annual peak. These results will help further understanding of the dynamics and chemistry of Mars atmosphere.