Algebra"Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduatelevel algebra books." NOTICES OF THE AMS "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bogged down in the dry formalism which pervades some parts of algebra." MATHEMATICAL REVIEWS This book is intended as a basic text for a oneyear course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higherlevel algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text. 
What people are saying  Write a review
User ratings
5 stars 
 
4 stars 
 
3 stars 
 
2 stars 
 
1 star 

very special book .ha............
Full disclosure: I am an undergraduate student teaching myself from Lang's 'Algebra' and I hope my review will help others who may be looking to do the same.
On the book, in general: Lang has some idiosyncrasies that build up over the course of this tome—namely, differences in terminology— but it is well worth having. His categorical approach is indispensable, you will have to learn it at some point if your mathematical pursuits point you in this direction. If you have the patience, time and diligence, it is well worth your while to work out the examples and problems in the text as they will significantly broaden your understanding and perception of the subject in a manner that other 'standard' texts like Dummit & Foote would not.
My personal experience:
On a more personal level, my complaints with this text are limited. Lang faces the classic dilemma of 'quality vs. quantity' and has decided on the latter, in that many of the 'proofs' in this text, while full and acceptable, are not 'fleshed out' in the interest of making the book <1600 pages long! So, I would not recommend this book as a starting 'kit' to teach oneself abstract algebra except for, perhaps, the most talented students. I am currently undertaking that task and I find it exceptionally challenging, and I am by no means amongst the most talented students. There are some things that Lang leaves to the reader that are not all that trivial. The reader will have to connect the dots to figure out what Lang means on many proofs and will be forced to draw on their knowledge from the preceeding sections to do so.
As an example, Lang may state that a particular morphism is injective and will give a little blurb on his reasoning that is moreorless a hint to reader on how to attack the issue of demonstrating his statement. Many of these sorts of statements, he presumes, will be obvious, and in many cases they are easily divined, but occasionally I find they are not. I believe this detracts from the overall quality of the book as a tool to teach yourself, but this should not be misconstrued as an attack on the book's worth. The text is obviously intended for a mathematically mature audience.
Lang's 'Algebra' is called a dry text. I can only comment on this by saying that if you are looking for an approach that actively attempts to engage readers, this is not it. However, the interested and selfmotivated reader should have no problem dealing with this, I certainly have never found it a problem. If you are confident in your abilities and willing to consult outside texts for help, I would say to use Lang's book as your primary resource. Perhaps you are talented enough to muscle your way through Lang alone! If you are less confident, I would recommend you do not pick up Lang's tome as your primary resource! Take your time with other books and return to Lang afterwards for a rewarding categorical and homological approach that is the basis of modern algebra!
Contents
I  3 
II  7 
III  13 
IV  23 
V  25 
VI  33 
VII  36 
VIII  42 
LXXXI  465 
LXXXII  468 
LXXXIII  476 
LXXXIV  480 
LXXXV  486 
LXXXVI  487 
LXXXVII  491 
LXXXVIII  503 
IX  46 
X  49 
XI  53 
XII  66 
XIII  83 
XIV  92 
XV  97 
XVI  107 
XVII  111 
XVIII  117 
XIX  122 
XX  127 
XXI  135 
XXII  139 
XXIII  142 
XXIV  146 
XXV  155 
XXVI  157 
XXVII  159 
XXVIII  173 
XXIX  180 
XXX  183 
XXXI  186 
XXXII  187 
XXXIII  190 
XXXIV  194 
XXXV  200 
XXXVI  205 
XXXVII  223 
XXXVIII  229 
XXXIX  235 
XL  239 
XLI  244 
XLII  247 
XLIII  261 
XLIV  269 
XLV  276 
XLVI  282 
XLVII  284 
XLVIII  288 
XLIX  291 
L  293 
LI  297 
LII  302 
LIII  304 
LIV  308 
LV  312 
LVI  313 
LVII  315 
LVIII  333 
LIX  340 
LX  346 
LXI  355 
LXII  357 
LXIII  360 
LXIV  363 
LXV  377 
LXVI  378 
LXVII  381 
LXVIII  388 
LXIX  402 
LXX  406 
LXXI  413 
LXXII  416 
LXXIII  421 
LXXIV  424 
LXXV  426 
LXXVI  431 
LXXVII  439 
LXXVIII  449 
LXXIX  451 
LXXX  457 
LXXXIX  506 
XC  507 
XCI  511 
XCII  522 
XCIII  527 
XCIV  531 
XCV  536 
XCVI  540 
XCVII  553 
XCVIII  556 
XCIX  561 
C  571 
CI  574 
CII  575 
CIII  577 
CIV  579 
CV  581 
CVI  584 
CVII  586 
CVIII  588 
CIX  589 
CX  594 
CXI  601 
CXII  607 
CXIII  612 
CXIV  623 
CXV  625 
CXVI  629 
CXVII  632 
CXVIII  635 
CXIX  641 
CXX  645 
CXXI  646 
CXXII  651 
CXXIII  654 
CXXIV  657 
CXXV  660 
CXXVI  663 
CXXVII  664 
CXXVIII  667 
CXXIX  671 
CXXX  673 
CXXXI  677 
CXXXII  686 
CXXXIII  688 
CXXXIV  699 
CXXXV  702 
CXXXVI  704 
CXXXVII  710 
CXXXVIII  712 
CXXXIX  731 
CXL  738 
CXLI  744 
CXLII  747 
CXLIII  761 
CXLIV  767 
CXLV  769 
CXLVI  782 
CXLVII  787 
CXLVIII  790 
CXLIX  799 
CL  806 
CLI  814 
CLII  835 
CLIII  839 
CLIV  846 
CLV  850 
CLVI  867 
CLVII  875 
895  
903  