We present the results of the first long-term (2.2 years) spectroscopic monitoring of a gravitationally lensed quasar, namely the Einstein Cross Q2237+0305. The goal of this paper is to present the observational facts to be compared in follow-up papers with theoretical models to constrain the inner structure of the source quasar. We spatially deconvolve deep VLT/FORS1 spectra to accurately separate the spectrum of the lensing galaxy from the spectra of the quasar images. Accurate cross-calibration of the 58 observations at 31-epoch from October 2004 to December 2006 is carried out with non-variable foreground stars observed simultaneously with the quasar. The quasar spectra are further decomposed into a continuum component and several broad emission lines to infer the variations of these spectral components. We find prominent microlensing events in the quasar images A and B, while images C and D are almost quiescent on a timescale of a few months. The strongest variations are observed in the continuum of image A. Their amplitude is larger in the blue (0.7 mag) than in the red (0.5 mag), consistent with microlensing of an accretion disk. Variations in the intensity and profile of the broad emission lines are also reported, most prominently in the wings of the CIII] and center of the CIV emission lines. During a strong microlensing episode observed in June 2006 in quasar image A, the broad component of the CIII] is more highly magnified than the narrow component. In addition, the emission lines with higher ionization potentials are more magnified than the lines with lower ionization potentials, consistent with the results obtained with reverberation mapping. Finally, we find that the V-band differential extinction by the lens, between the quasar images, is in the range 0.1-0.3 mag.
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