This book presents both long-standing and recent mathematical results from this field in a uniform way. It focuses on exact analytic formulas for reconstructing a function or a vector field from data of integrals over lines, rays, circles, arcs, parabolas, hyperbolas, planes, hyperplanes, spheres, and paraboloids. The book also addresses range characterizations and collects necessary definitions and elementary facts from geometry and analysis. Coverage is motivated by both applications and pure mathematics.