Explore the depths of geometric analysis on Riemannian symmetric spaces with “Geometric Analysis on Symmetric Spaces” by Sigurdur Helgason, a cornerstone text from The Bookish Owl. This revised edition offers a systematic exposition, bridging geometric analysis and the representation theory of Lie groups. Delve into modern integral geometry, Radon and Fourier transforms on symmetric spaces, and their inversion formulas. Discover applications to invariant differential equations, potential theory, and wave equations, including the canonical multitemporal wave equation. The book concludes with Eigen space representations, making it an ideal resource for advanced graduate students and researchers in integral geometry, analysis on Lie groups, and Lie group representation theory. Featuring exercises with solutions and extensive references, this edition enhances understanding of complex mathematical concepts.