Preliminary results of the inversion of spectropolarimetric maps of a sunspot observed with the Advanced Stokes Polarimeter (ASP) are presented. The method used, Stokes Inversion based on Response functions (SIR), does not assume constancy of the different parameters with depth, thus enabling us to embark on an analysis of the information at different layers in continuum optical depth (i.e. optical tomography), of a sunspot's photosphere. Maps of the vector magnetic field and other physical quantities like temperature or line-of-sight velocity at several optical depths show a new and promising view of the structure of a sunspot, casting light on long standing debates as those over penumbral `corrugated' fields (spines), superpenumbral canopies, return flux, or the nature of the Evershed effect.