From the reviews: "The history of investigations of real numbers is the starting point of this monograph. ... Every chapter is supplied with a well-chosen series of exercises containing interesting complementary material. ... This unique monograph presents beautiful scientific work prepared in a professional style and built upon a number of references to prominent mathematicians living in previous epochs ... . A wide variety of researchers and students will find in it a large ... attractive body of knowledge that should be highly inspiring in their work." (Marek Balcerzak, Mathematical Reviews, Issue 2012 d) "The book under review is addressed to experts and begins to address some of the questions about the complexities of the real line. ... The author provides an appendix with background material on set theory, algebra, topology and metamathematics." (William J. Satzer, The Mathematical Association of America, August, 2011)

• Preface.- 1 Introduction.- 2 The Real Line.- 3 Topology of Euclidean Spaces.- 4 Measure Theory.- 5 Useful Tools and Technologies.- 6 Descriptive Set Theory.- 7 Decline and Fall of the Duality.- 8 Special Sets of Reals.- 9 Additional Axioms.- 10 Undecidable Statements.- 11 Appendix.- Bibliography.- Index of Notation.- Index.

From the reviews: "The history of investigations of real numbers is the starting point of this monograph. ... Every chapter is supplied with a well-chosen series of exercises containing interesting complementary material. ... This unique monograph presents beautiful scientific work prepared in a professional style and built upon a number of references to prominent mathematicians living in previous epochs ... . A wide variety of researchers and students will find in it a large ... attractive body of knowledge that should be highly inspiring in their work." (Marek Balcerzak, Mathematical Reviews, Issue 2012 d) "The book under review is addressed to experts and begins to address some of the questions about the complexities of the real line. ... The author provides an appendix with background material on set theory, algebra, topology and metamathematics." (William J. Satzer, The Mathematical Association of America, August, 2011)

• Preface.- 1 Introduction.- 2 The Real Line.- 3 Topology of Euclidean Spaces.- 4 Measure Theory.- 5 Useful Tools and Technologies.- 6 Descriptive Set Theory.- 7 Decline and Fall of the Duality.- 8 Special Sets of Reals.- 9 Additional Axioms.- 10 Undecidable Statements.- 11 Appendix.- Bibliography.- Index of Notation.- Index.

From the reviews: "The history of investigations of real numbers is the starting point of this monograph. ... Every chapter is supplied with a well-chosen series of exercises containing interesting complementary material. ... This unique monograph presents beautiful scientific work prepared in a professional style and built upon a number of references to prominent mathematicians living in previous epochs ... . A wide variety of researchers and students will find in it a large ... attractive body of knowledge that should be highly inspiring in their work." (Marek Balcerzak, Mathematical Reviews, Issue 2012 d) "The book under review is addressed to experts and begins to address some of the questions about the complexities of the real line. ... The author provides an appendix with background material on set theory, algebra, topology and metamathematics." (William J. Satzer, The Mathematical Association of America, August, 2011)

• Preface.- 1 Introduction.- 2 The Real Line.- 3 Topology of Euclidean Spaces.- 4 Measure Theory.- 5 Useful Tools and Technologies.- 6 Descriptive Set Theory.- 7 Decline and Fall of the Duality.- 8 Special Sets of Reals.- 9 Additional Axioms.- 10 Undecidable Statements.- 11 Appendix.- Bibliography.- Index of Notation.- Index.