Very recently a new inversion method has been developped to analyze the intergalactic medium seen in absorption in quasar spectra ( the so-called Lyman- \alpha forest ) .
This method is applied to recover the temperature of the gas and the underlying density field .
Using constraints from the Lyman- \beta forest , it is possible to recover this field up to over-densities \delta \sim 10 .
By inverting the H i and C iv absorptions together it has been shown that the C iv /H i ratio varies through the profile of strong lines , beeing larger in the wings .
The method can be applied to reconstruct the 3D density field from multiple lines of sight and is shown to give good results up to mean separations of 3 arcmin .
Results from a survey of QSO pairs performed with HST/STIS and VLT/UVES-FORS are summarized .