Joram Lindenstrauss is professor emeritus of mathematics at the Hebrew University of Jerusalem. David Preiss is professor of mathematics at the University of Warwick. Jaroslav Ti er is associate professor of mathematics at Czech Technical University in Prague.

"The book is well written--as one would expect from its distinguished authors, including the late Joram Lindestrauss (1936-2012). It contains many fascinating and profound results. It no doubt will become an important resource for anyone who is seriously interested in the differentiability of functions between Banach spaces."--J. Borwein and Liangjin Yao, Mathematical Reviews Clippings "[T]his is a very deep and complete study on the differentiability of Lipschitz mappings between Banach spaces, an unavoidable reference for anyone seriously interested in this topic."--Daniel Azagra, European Mathematical Society "We should be grateful to (the late) Joram Lindenstrauss, David Preiss, and Jaroslav Tiser for providing us with this splendid book which dives into the deepest fields of functional analysis, where the basic but still strange operation called differentiation is investigated. More than a century after Lebesgue, our understanding is not complete. But thanks to the contribution of these three authors, and thanks to this book, we know a fair share of beautiful theorems and challenging problems."--Gilles Godefroy, Bulletin of the American Mathematical Society

• *FrontMatter, pg. i*Contents, pg. vii*Chapter One: Introduction, pg. 1*Chapter Two: Gateaux differentiability of Lipschitz functions, pg. 12*Chapter Three: Smoothness, convexity, porosity, and separable determination, pg. 23*Chapter Four: epsilon-Frechet differentiability, pg. 46*Chapter Five: GAMMA-null and GAMMAn-null sets, pg. 72*Chapter Six: Ferchet differentiability except for GAMMA-null sets, pg. 96*Chapter Seven: Variational principles, pg. 120*Chapter Eight: Smoothness and asymptotic smoothness, pg. 133*Chapter Nine: Preliminaries to main results, pg. 156*Chapter Ten: Porosity, GAMMAn- and GAMMA-null sets, pg. 169*Chapter Eleven: Porosity and epsilon-Frechet differentiability, pg. 202*Chapter Twelve: Frechet differentiability of real-valued functions, pg. 222*Chapter Thirteen: Frechet differentiability of vector-valued functions, pg. 262*Chapter Fourteen: Unavoidable porous sets and nondifferentiable maps, pg. 319*Chapter Fifteen: Asymptotic Frechet differentiability, pg. 355*Chapter Sixteen: Differentiability of Lipschitz maps on Hilbert spaces, pg. 392*Bibliography, pg. 415*Index, pg. 419*Index of Notation, pg. 423

Joram Lindenstrauss is professor emeritus of mathematics at the Hebrew University of Jerusalem. David Preiss is professor of mathematics at the University of Warwick. Jaroslav Ti er is associate professor of mathematics at Czech Technical University in Prague.

"The book is well written--as one would expect from its distinguished authors, including the late Joram Lindestrauss (1936-2012). It contains many fascinating and profound results. It no doubt will become an important resource for anyone who is seriously interested in the differentiability of functions between Banach spaces."--J. Borwein and Liangjin Yao, Mathematical Reviews Clippings "[T]his is a very deep and complete study on the differentiability of Lipschitz mappings between Banach spaces, an unavoidable reference for anyone seriously interested in this topic."--Daniel Azagra, European Mathematical Society "We should be grateful to (the late) Joram Lindenstrauss, David Preiss, and Jaroslav Tiser for providing us with this splendid book which dives into the deepest fields of functional analysis, where the basic but still strange operation called differentiation is investigated. More than a century after Lebesgue, our understanding is not complete. But thanks to the contribution of these three authors, and thanks to this book, we know a fair share of beautiful theorems and challenging problems."--Gilles Godefroy, Bulletin of the American Mathematical Society

• *FrontMatter, pg. i*Contents, pg. vii*Chapter One: Introduction, pg. 1*Chapter Two: Gateaux differentiability of Lipschitz functions, pg. 12*Chapter Three: Smoothness, convexity, porosity, and separable determination, pg. 23*Chapter Four: epsilon-Frechet differentiability, pg. 46*Chapter Five: GAMMA-null and GAMMAn-null sets, pg. 72*Chapter Six: Ferchet differentiability except for GAMMA-null sets, pg. 96*Chapter Seven: Variational principles, pg. 120*Chapter Eight: Smoothness and asymptotic smoothness, pg. 133*Chapter Nine: Preliminaries to main results, pg. 156*Chapter Ten: Porosity, GAMMAn- and GAMMA-null sets, pg. 169*Chapter Eleven: Porosity and epsilon-Frechet differentiability, pg. 202*Chapter Twelve: Frechet differentiability of real-valued functions, pg. 222*Chapter Thirteen: Frechet differentiability of vector-valued functions, pg. 262*Chapter Fourteen: Unavoidable porous sets and nondifferentiable maps, pg. 319*Chapter Fifteen: Asymptotic Frechet differentiability, pg. 355*Chapter Sixteen: Differentiability of Lipschitz maps on Hilbert spaces, pg. 392*Bibliography, pg. 415*Index, pg. 419*Index of Notation, pg. 423