Context : The Taurus Molecular Cloud ( TMC ) is the nearest large star-forming region , prototypical for the distributed mode of low-mass star formation . Pre-main sequence stars are luminous X-ray sources , probably mostly owing to magnetic energy release . Aims : The XMM-Newton Extended Survey of the Taurus Molecular Cloud ( XEST ) presented in this paper surveys the most populated \approx 5 square degrees of the TMC , using the XMM-Newton X-ray observatory to study the thermal structure , variability , and long-term evolution of hot plasma , to investigate the magnetic dynamo , and to search for new potential members of the association . Many targets are also studied in the optical , and high-resolution X-ray grating spectroscopy has been obtained for selected bright sources . Methods : The X-ray spectra have been coherently analyzed with two different thermal models ( 2-component thermal model , and a continuous emission measure distribution model ) . We present overall correlations with fundamental stellar parameters that were derived from the previous literature . A few detections from Chandra observations have been added . Results : The present overview paper introduces the project and provides the basic results from the X-ray analysis of all sources detected in the XEST survey . Comprehensive tables summarize the stellar properties of all targets surveyed . The survey goes deeper than previous X-ray surveys of Taurus by about an order of magnitude and for the first time systematically accesses very faint and strongly absorbed TMC objects . We find a detection rate of 85 % and 98 % for classical and weak-line T Tau stars ( CTTS resp . WTTS ) , and identify about half of the surveyed protostars and brown dwarfs . Overall , 136 out of 169 surveyed stellar systems are detected . We describe an X-ray luminosity vs. mass correlation , discuss the distribution of X-ray-to-bolometric luminosity ratios , and show evidence for lower X-ray luminosities in CTTS compared to WTTS . Detailed analysis ( e.g. , variability , rotation-activity relations , influence of accretion on X-rays ) will be discussed in a series of accompanying papers . Conclusions :