“In every field of mathematics there are monographs describing the present knowledge in that area. … the book under review does exactly this for the theory of Banach spaces. … At the end of the book there are an extended and very useful subject index and an alphabetical list of concepts and problems that help the reader to locate problems involving a particular topic. … attractive to researchers in Banach space theory and to prospective PhD students in this field.” (Dirk Werner, zbMATH 1351.46001, 2017)“The book is very well organized - every problem is preceded by an introductory part containing the notions and previous results necessary for its understanding, as well as references to significant papers or books containing partial solutions or related results. … All in all, the authors produced a marvelous piece of mathematical writing of great use for researchers in various fields of functional and mathematical analysis as well as for young graduate or PhD students.” (S. Cobzaş, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 61 (4), 2016)

• Preface.- Basic linear structure.- Basic linear geometry.- Biorthogonal systems.- Smoothness, smooth approximation.- Nonlinear geometry.- Some more nonseparable problems.- Some applications.- Bibliography.- List of concepts and problems.- Symbol index.- Subject index.

“In every field of mathematics there are monographs describing the present knowledge in that area. … the book under review does exactly this for the theory of Banach spaces. … At the end of the book there are an extended and very useful subject index and an alphabetical list of concepts and problems that help the reader to locate problems involving a particular topic. … attractive to researchers in Banach space theory and to prospective PhD students in this field.” (Dirk Werner, zbMATH 1351.46001, 2017)“The book is very well organized - every problem is preceded by an introductory part containing the notions and previous results necessary for its understanding, as well as references to significant papers or books containing partial solutions or related results. … All in all, the authors produced a marvelous piece of mathematical writing of great use for researchers in various fields of functional and mathematical analysis as well as for young graduate or PhD students.” (S. Cobzaş, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 61 (4), 2016)

• Preface.- Basic linear structure.- Basic linear geometry.- Biorthogonal systems.- Smoothness, smooth approximation.- Nonlinear geometry.- Some more nonseparable problems.- Some applications.- Bibliography.- List of concepts and problems.- Symbol index.- Subject index.

“In every field of mathematics there are monographs describing the present knowledge in that area. … the book under review does exactly this for the theory of Banach spaces. … At the end of the book there are an extended and very useful subject index and an alphabetical list of concepts and problems that help the reader to locate problems involving a particular topic. … attractive to researchers in Banach space theory and to prospective PhD students in this field.” (Dirk Werner, zbMATH 1351.46001, 2017)“The book is very well organized - every problem is preceded by an introductory part containing the notions and previous results necessary for its understanding, as well as references to significant papers or books containing partial solutions or related results. … All in all, the authors produced a marvelous piece of mathematical writing of great use for researchers in various fields of functional and mathematical analysis as well as for young graduate or PhD students.” (S. Cobzaş, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 61 (4), 2016)

• Preface.- Basic linear structure.- Basic linear geometry.- Biorthogonal systems.- Smoothness, smooth approximation.- Nonlinear geometry.- Some more nonseparable problems.- Some applications.- Bibliography.- List of concepts and problems.- Symbol index.- Subject index.