Mathematical Methods in Tomography : Proceedings of a Conference held in Oberwolfach Germany 5–11 June 1990 The conference was devoted to the discussion of present and future techniques in medical imaging including 3D x ray CT ultrasound and diffraction tomography and biomagnetic ima ging. The mathematical models their theoretical aspects and the development of algorithms were treated. The proceedings contains surveys on reconstruction in inverse obstacle scat tering inversion in 3D and constrained least squares pro blems.Research papers include besides the mentioned imaging techniques presentations on image reconstruction in Hilbert spaces singular value decompositions 3D cone beam recon struction diffuse tomography regularization of ill posed problems evaluation reconstruction algorithms and applica tions in non medical fields. Contents: Theoretical Aspects: J.Boman: Helgason s support theorem for Radon transforms a newproof and a generalization P.Maass: Singular value de compositions for Radon transforms W.R.Madych: Image recon struction in Hilbert space R.G.Mukhometov: A problem of in tegral geometry for a family of rays with multiple reflec tions V.P.Palamodov: Inversion formulas for the three di mensional ray transform Medical Imaging Techniques: V.Friedrich: Backscattered Photons are they useful for a surface near tomography P.Grangeat: Mathematical frame work of cone beam 3D reconstruction via the first derivative of the Radon transform P.Grassin B.Duchene W.Tabbara: Dif fraction tomography: some applications and extension to 3D ultrasound imaging F.A.Gr}nbaum: Diffuse tomography: a re fined model R.Kress A.Zinn: Three dimensional reconstruc tions in inverse obstacle scattering A.K.Louis: Mathemati cal questions of a biomagnetic imaging problem Inverse Problems and Optimization: Y.Censor: On variable block algebraic reconstruction techniques P.P.Eggermont: On Volterra Lotka differential equations and multiplicative algorithms for monotone complementary problems