  We solve the inverse spectral problems for the class of Sturm--Liouville
operators with singular real-valued potentials from the Sobolev space
W^{s-1}_2(0,1), s\in[0,1]. The potential is recovered from two spectra or from
the spectrum and norming constants. Necessary and sufficient conditions on the
spectral data to correspond to the potential in W^{s-1}_2(0,1) are established.
