A collection of invited chapters dedicated to Carlos Segovia, this unified and self-contained volume examines recent developments in real and harmonic analysis. The work begins with a chronological description of Segovias mathematical life, highlighting his original ideas and their evolution. Also included are surveys dealing with Carlos favorite topics, and PDE works written by students and colleagues close to Segovia whose careers were in some way influenced by him. Specific topics covered include: Vector-valued singular integral equations; Harmonic analysis related to Hermite expansions; Gas flow in porous media; Global well-posedness of the KPI Equation; MongeAmpère type equations and applications; Spaces of homogeneous type; Hardy and Lipschitz spaces; One-sided operators. Contributors: H. Aimar, A. Bonami, O. Blasco, L.A. Caffarelli, S. Chanillo, J. Feuto, L. Forzani, C.E. Gutíerrez, E. Harboure, A.L. Karakhanyan, C.E. Kenig, R.A. Macías, J.J. Manfredi, F.J. Martín-Reyes, P. Ortega, R. Scotto, A. de la Torre, J.L. Torrea.

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