Customer Rating: 
Summary: Dated and verbose
Comment: Writing about analysis has come a long way since the days of Hardy. There are a number of modern books on the topic with clear, vigorous prose that is lacking in Hardy and provide better coverage. But to be fair, mathematics is a developing endeavor and you'd expect improvements during 100 years. Mostly a curiosity. I believe you can read it online for free.
Customer Rating:
Summary: An Enduring Classic
Comment: G. H. Hardy was one of the greatest mathematicians of the 20th century. When the first edition of this book appeared in 1908, it was the only comprehensive introduction to analysis in the English language. Nearly a century later, it remains unsurpassed in that genre in any language.
Elegant, detailed and precise, with perfect prose and proofs, and numerous examples, it reveals the talents of a master mathematician and pedagogue.
I weep in frustration when I see the ridiculous number of poorly conceived and hideously expensive freshman calculus texts whose only claim to modernity are coloured boxes surrounding the equations. The reader patient enough to work through the many exercises in this magnificent volume will have a firm grounding in elementary analysis and feel the immense joy of pure mathematics.
P.S. If you are a first year mathematics student and your faculty expects you to squander your money on one of those "paper weight" calculus books, you should complain loudly!
Customer Rating:
Summary: Hard Core Math
Comment: This book is very hard core. I bought it to help with the math in Penrose's Road to Reality. Which is really hard core. So now I need a math book to help with the math in this book. As far as my ability allows I fully agree with the other 5 star reviews of this book.
Customer Rating:
Summary: Best introduction to mathematical analysis
Comment: This book is simply beyond any rating whatsoever. Giving 5 stars is to undermine the value of this classic.
The first time I got this book, I was neither aware of it not of its author. I just picked it up randomly from school library. From the contents I figured it was a book on calculus. I immediately searched for the proof that "every continuous function is integrable." This was the first book I encountered which had a rigorous proof of this.
Then I began reading the chapters sequentially thinking that this seems to be a good book on calculus. The book went much beyond my expectation and it satisfied all my mathematical curiousities. All the mysteries of calculus were revelaed. Hardy demystified calculus in the first chapter itself by creating reals out ot rationals.
The Dedekind's construction of reals as presented in this book is the best I have seen. The properties of reals were not stated as axioms (common approach in books on analysis) but rather deduced from those of rationals.
The concepts of functions, limits, continuity, derivative etc. were explained in a prosaic style which has no parallel. This was also my first book on maths which had far more english words than mathematical symbols.
After finishing the entire book I was wondering who was this guy G. H. Hardy who has written such a masterpiece.
Only a few months later I came to know that he was one of the greatest British mathematicians of the century and was responsible for making our Indian Ramanujan famous. After that I read most of his books including "A Mathematician's Apology" and "An Introduction to Theory of Numbers"
Any persons who thinks maths is dull should just read few pages from this book and I bet his old beliefs would be shattered.
Customer Rating:
Summary: 1900 yrs from now....
Comment: ...people will look at this like we look at Euclid's Elements today, it's just one of those immortal books. Hardy starts by constructing the real numbers & then doing all the calculus you'd ever want to know, and with a bunch of math 'trivia' that can't be found anywhere. I can't add much to what the other reviewers have said, except this book has some evil integrals from old Cambridge Tripos exams that would make some Putnam problems look easy. lol At least, if you're only allowed to use real variables (& not complex variables & residues). Get this book for an excellent reference no matter what level you're at.
Summary: Dated and verbose
Comment: Writing about analysis has come a long way since the days of Hardy. There are a number of modern books on the topic with clear, vigorous prose that is lacking in Hardy and provide better coverage. But to be fair, mathematics is a developing endeavor and you'd expect improvements during 100 years. Mostly a curiosity. I believe you can read it online for free.
Customer Rating:
Summary: An Enduring Classic
Comment: G. H. Hardy was one of the greatest mathematicians of the 20th century. When the first edition of this book appeared in 1908, it was the only comprehensive introduction to analysis in the English language. Nearly a century later, it remains unsurpassed in that genre in any language.
Elegant, detailed and precise, with perfect prose and proofs, and numerous examples, it reveals the talents of a master mathematician and pedagogue.
I weep in frustration when I see the ridiculous number of poorly conceived and hideously expensive freshman calculus texts whose only claim to modernity are coloured boxes surrounding the equations. The reader patient enough to work through the many exercises in this magnificent volume will have a firm grounding in elementary analysis and feel the immense joy of pure mathematics.
P.S. If you are a first year mathematics student and your faculty expects you to squander your money on one of those "paper weight" calculus books, you should complain loudly!
Customer Rating:
Summary: Hard Core Math
Comment: This book is very hard core. I bought it to help with the math in Penrose's Road to Reality. Which is really hard core. So now I need a math book to help with the math in this book. As far as my ability allows I fully agree with the other 5 star reviews of this book.
Customer Rating:
Summary: Best introduction to mathematical analysis
Comment: This book is simply beyond any rating whatsoever. Giving 5 stars is to undermine the value of this classic.
The first time I got this book, I was neither aware of it not of its author. I just picked it up randomly from school library. From the contents I figured it was a book on calculus. I immediately searched for the proof that "every continuous function is integrable." This was the first book I encountered which had a rigorous proof of this.
Then I began reading the chapters sequentially thinking that this seems to be a good book on calculus. The book went much beyond my expectation and it satisfied all my mathematical curiousities. All the mysteries of calculus were revelaed. Hardy demystified calculus in the first chapter itself by creating reals out ot rationals.
The Dedekind's construction of reals as presented in this book is the best I have seen. The properties of reals were not stated as axioms (common approach in books on analysis) but rather deduced from those of rationals.
The concepts of functions, limits, continuity, derivative etc. were explained in a prosaic style which has no parallel. This was also my first book on maths which had far more english words than mathematical symbols.
After finishing the entire book I was wondering who was this guy G. H. Hardy who has written such a masterpiece.
Only a few months later I came to know that he was one of the greatest British mathematicians of the century and was responsible for making our Indian Ramanujan famous. After that I read most of his books including "A Mathematician's Apology" and "An Introduction to Theory of Numbers"
Any persons who thinks maths is dull should just read few pages from this book and I bet his old beliefs would be shattered.
Customer Rating:
Summary: 1900 yrs from now....
Comment: ...people will look at this like we look at Euclid's Elements today, it's just one of those immortal books. Hardy starts by constructing the real numbers & then doing all the calculus you'd ever want to know, and with a bunch of math 'trivia' that can't be found anywhere. I can't add much to what the other reviewers have said, except this book has some evil integrals from old Cambridge Tripos exams that would make some Putnam problems look easy. lol At least, if you're only allowed to use real variables (& not complex variables & residues). Get this book for an excellent reference no matter what level you're at.