Provides an historical overview of several decades in integral geometry and geometric analysis as well as recent advances in these fields and closely related areas. It contains several articles focusing on the mathematical work of Sigurdur Helgason, including an overview of his research by Gestur Olafsson and Robert Stanton.

Historical articles: Some personal remarks on the Radon transform by S. HelgasonOn the life and work of S. Helgason by G. Olafsson and R. J. StantonResearch and expository articles: Microlocal analysis of an ultrasound transform with circular source and receiver trajectories by G. Ambartsoumian, J. Boman, V. P. Krishnan, and E. T. QuintoCuspidal discrete series for projective hyperbolic spaces by N. B. Andersen and M. Flensted-JensenThe Radon transform on $SO(3)$: Motivations, generalizations, discretization by S. Bernstein and I. Z. PesensonAtomic decompositions of Besov spaces related to symmetric cones by J. G. ChristensenA double fibration transform for complex projective space by M. EastwoodMagnetic Schrodinger equation on compact symmetric spaces and the geodesic Radon transform of one forms by T. Kakehi$F$-method for constructing equivariant differential operators by T. KobayashiSchiffer's conjecture, interior transmission eigenvalues and invisibility cloaking: Singular problem vs. nonsingular problem by H. LiuApproximate reconstruction from circular and spherical mean Radon transform data by W. R. MadychAnalytic and group-theoretic aspects of the cosine transform by G. Olafsson, A. Pasquale, and B. RubinQuantization of linear algebra and its application to integral geometry by H. Oda and T. OshimaMean value theorems on symmetric spaces by F. RouviereSemyanistyi fractional integrals and Radon transforms by B. RubinRadon-Penrose transform between symmetric spaces by H. SekiguchiPrincipal series representations of infinite dimensional Lie groups, II: construction of induced representations by J. A. Wolf