In this book， we list and introduce some interesting， important or useful mathematics books. Most selected books were published during the twentieth century. For the convenience of the reader， we have arranged books according to topics. Besides some introductions and comments， we also quote from informative reviews of these books from sources including MathSciNet， Zentralblatt Math and the Bulletin of the American Mathematica Society. A common way for people to pick out books to read is to follow recommendations of either book reviews or experts. The list of books is probably the most interesting part of this book， Once the titles or authors' names are known， it is relatively easy to find valuable information and reviews about the book from many different sources （but it might take some efforts to find good books on subjects outside one's expertise.） In spite of this， we hope that additional information provided here about these books might be helpful and convenient.
lizhen ji is a professor of mathematics at university of michigan and studies subjects related to lie groups， discrete subgroups of lie groups， transformation groups and related spaces. he loves books and is a chief-editor of four book series： advanced lectures in mathematics， mathematics and humanities， panorama of mathematics， surveys of modern mathematics， and of the journal pure and applied mathematics quarterly. he is also an editor of journals asian journal of mathematics and science in china： mathematics.
he was a sloan fellow and received the nsf postdoctoral fellowship and the morningside silver medal of mathematics. he enjoys listening to good mathematics talks on diverse topics and has organized over 30 summer schools， conferences or workshops. he is also an active organizer of seminars and colloquiums. for example， he is the organizer of one of the first seminars called “what is ...” in the world.
1、Introduction
2、Expository Books On Mathematics And Mathematicians
2.1 Popular And Expository Books On Mathematics
2.1.1 R. Courant, H.Robbins, What Is Mathematics? Oxford University Press, New York, 1941. Xix+521 Pp
2.1.2 A.D. Aleksandrov, A.N. Kolmogorov, M.A. Lavrent'ev, Mathematics： Its Content, Methods, And Meaning. Vol.I, Vol. Ii, Vol. Iii, The M.I.T. Press, Cambridge, Mass., 1963, Xi+359 Pp.; Xi+377 Pp.; Xi+356 Pp.. Translated By S.H. Gould And T. Bartha; S.H. Gould; K. Hirsch
2.1.3 G. P\'Olya, How To Solve It. A New Aspect Of Mathematical Method. Expanded Version Of The 1988 Edition, With A New Foreword By John H. Conway, Princeton Science Library, Princeton University Press, 2004. Xxviii+253 Pp
2.1.4 G.H. Hardy, A Mathematician's Apology, With A Foreword By C.P. Snow, Reprint Of The 1967 Edition, Canto, Cambridge University Press, Cambridge, 1992
2.1.5 J.E. Littlewood, Littlewood's Miscellany, Edited And With A Foreword By Bola Bollobas, Cambridge University Press, Cambridge, 1986. Vi+200 Pp
2.1.6 Autobiographies Of Mathematicians
2.1.7 H. Weyl, Symmetry. Reprint Of The 1952 Original. Princeton Science Library. Princeton University Press, Princeton, N.J.,1989
2.1.8 D. Hilbert, S. Cohn-Vossen, Geometry And The Imagination, American Mathematical Society, 1, 1999. 357 Pages
2.2 Biographies Of Mathematicians And History Of Mathematics
2.2.1 E.T. Bell, Men Of Mathematics, Touchstone, 1986. 608 Pages 1、Introduction
2、Expository Books On Mathematics And Mathematicians
2.1 Popular And Expository Books On Mathematics
2.1.1 R. Courant, H.Robbins, What Is Mathematics? Oxford University Press, New York, 1941. Xix+521 Pp
2.1.2 A.D. Aleksandrov, A.N. Kolmogorov, M.A. Lavrent'ev, Mathematics： Its Content, Methods, And Meaning. Vol.I, Vol. Ii, Vol. Iii, The M.I.T. Press, Cambridge, Mass., 1963, Xi+359 Pp.; Xi+377 Pp.; Xi+356 Pp.. Translated By S.H. Gould And T. Bartha; S.H. Gould; K. Hirsch
2.1.3 G. P\'Olya, How To Solve It. A New Aspect Of Mathematical Method. Expanded Version Of The 1988 Edition, With A New Foreword By John H. Conway, Princeton Science Library, Princeton University Press, 2004. Xxviii+253 Pp
2.1.4 G.H. Hardy, A Mathematician's Apology, With A Foreword By C.P. Snow, Reprint Of The 1967 Edition, Canto, Cambridge University Press, Cambridge, 1992
2.1.5 J.E. Littlewood, Littlewood's Miscellany, Edited And With A Foreword By Bola Bollobas, Cambridge University Press, Cambridge, 1986. Vi+200 Pp
2.1.6 Autobiographies Of Mathematicians
2.1.7 H. Weyl, Symmetry. Reprint Of The 1952 Original. Princeton Science Library. Princeton University Press, Princeton, N.J.,1989
2.1.8 D. Hilbert, S. Cohn-Vossen, Geometry And The Imagination, American Mathematical Society, 1, 1999. 357 Pages
2.2 Biographies Of Mathematicians And History Of Mathematics
2.2.1 E.T. Bell, Men Of Mathematics, Touchstone, 1986. 608 Pages
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3、Analysis
4、Algebra
5、Geometry
6、Topology
7、Number Theory
8、Differential Equations
9、Lie Theories
10、Mathematical Physics, Dynamical Systems And Ergodic Theory
11、Discrete Mathematics And Combinatorics
12、Probability And Applications
13、Foundations Of Math, Computer Science, Numerical Math
Stewart is a famous writer of popular mathematics， and this book is probably one of the best books he has written. Though it covers many standard topics related to group theory and symmetry， his broad knowledge about history and mathematics makes this a unique book among many books on symmetry.
According to MathSciNet， "Ian Stewart has written a story about symmetry and its role in mathematics and physics， beginning with the Babylonians and ending with modern physics. It's a book for the non- mathematician who would like to learn something about the nature of mathematics， and so perhaps there is no better subject for such a book than symmetry， an enticing property that is well known to most readers through art and music. But Stewart's book is not a picture book， though it is well illustrated. Neither does it contain many formulas， though the author treats mathematics in a serious way. The book's intention is to describe what symmetry means to mathematicians and why it has played such an important role throughout the ages in both mathematics and physics. The reader begins to see why and how abstract mathematical thought is intimately connected with truth， beauty， and the nature of the physical universe. The author also entertains the reader with stories about the 'muddle of mathematicians' we meet as the story unfolds."
According to Publishers Weekly， "while the math behind symmetry is important， the heart of this history lies in its characters， from a hypothetical Babylonian scribe with a serious case of math anxiety， through Evariste Galois （inventor of 'group theory'）， killed at 21 in a duel， and William Hamilton， whose eureka moment came in 'a flash of intuition that caused him to vandalize a bridge，' to Albert Einstein and the quantum physicists who used group theory and symmetry to describe the universe." J. Rosen， Sym'metry Discovered： Concepts and Applications in Nature and Science， Revised reprint of the 1975 original， Dover Publications， Inc.， Mineola， NY， 1998. xiv+152 pp.This is a good introduction to group theory and applications of symmetry. It is elementary， and concepts and definitions are carefully explained. According to MathSciNet，"This is an entertaining introduction to geometrical representations of discrete groups， enlivened by abundant illustrations and delightfully relevant quotations from books byA. A. Milne. The concept of symmetry is extended from isometries to similarities， and from geometry to physicsi music and biology. Thus the book might be regarded as amodern counterpart for H. Weyl's book Sy'm'metry " '， though it lacks Weyl's polished style."
Rosen is a physicist and has also written other books on group theory and symmetry. The basic point of these books is that science does not only make use of symmetry，but is essentially symmetry. Indeed， science builds on the foundation of reproducibility， predictability， and reduction， all of which are symmetries.
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