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This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems.

In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena.

Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book´s style and layout make it suitable for use in several courses, while its self-contained character makes it appropriate for self-study.

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Sets, Orders, Relations and Measures.- Encounters With Limits.- Elements of Functional Analysis.- Hilbert Spaces.- The Power of Differential Calculus.- A Touch of Convex Analysis.- Integration.- Differentiation and Integration.- Partial Differential Equations.- Evolution Problems.- References.- Index.

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"The topics it deals with are treated rather deeply, much beyond the needs required by their applicability. As a result, this book may be very useful to a large variety of readers, including professional mathematicians, graduate students and researchers and practitioners in many fields. ... In summary, this is an excellent book. ... I recommend it to every mathematical analyst, every applied mathematician, and every other user of mathematical analysis." (Juan Enrique Martínez-Legaz, Mathematical Reviews, 2018)

"This textbook is mainly intended for advanced undergraduate and graduate students, engineers as well as practitioners who want to be familiar with concepts and applications of analysis. ... The book it suitable for use in several courses, and its self-contained character make it appropriate for self-study." (Petr Gurka, zbMATH, Vol. 1366.26002, 2017)

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Jean-Paul Penot has published about 250 research articles and two books, including Calculus Without Derivatives, Graduate Texts in Mathematics Volume 266, Springer. He has taught in Paris (France), Sherbrooke (Canada), Pau (France) and participated in numerous conferences. His research interests include global analysis, optimization, convex analysis and nonsmooth analysis.

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