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This comprehensive introduction contains a thorough exploration of Radon transforms and related operators when the basic manifolds are the real Euclidean space, the unit sphere, and the real hyperbolic space. Radon-like transforms are discussed not only on smooth functions but also in the general context of Lebesgue spaces. Applications, open problems, and recent results are also included. The book will be useful for researchers in integral geometry, harmonic analysis, and related branches of mathematics. Fields of application include modern analysis, integral and convex geometry, and medical imaging. The text contains many examples and detailed proofs, making it accessible to graduate students and advanced undergraduates. The new edition includes four new chapters covering topics including integral geometry on lower-dimensional surfaces, tangency problems in integral geometry, and applications to convex geometry.