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. 
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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  5 
IV  9 
V  15 
VI  25 
VII  27 
VIII  35 
IX  38 
X  44 
XCII  467 
XCIV  470 
XCV  478 
XCVI  482 
XCVII  488 
XCVIII  489 
XCIX  493 
C  505 
XI  48 
XII  51 
XIII  55 
XIV  68 
XV  85 
XVII  94 
XVIII  99 
XIX  109 
XX  113 
XXI  119 
XXII  124 
XXIII  129 
XXIV  137 
XXV  141 
XXVI  144 
XXVII  148 
XXVIII  157 
XXIX  159 
XXX  161 
XXXI  175 
XXXIII  182 
XXXIV  185 
XXXV  188 
XXXVI  189 
XXXVII  192 
XXXVIII  196 
XXXIX  202 
XL  207 
XLI  225 
XLIV  231 
XLV  237 
XLVI  241 
XLVII  246 
XLVIII  249 
XLIX  263 
LI  271 
LII  278 
LIII  284 
LIV  286 
LV  290 
LVI  293 
LVII  295 
LVIII  299 
LIX  304 
LX  306 
LXI  310 
LXII  314 
LXIII  315 
LXIV  317 
LXV  335 
LXVII  342 
LXVIII  348 
LXIX  357 
LXX  359 
LXXI  362 
LXXII  365 
LXXIII  379 
LXXIV  380 
LXXV  383 
LXXVI  390 
LXXVII  404 
LXXVIII  408 
LXXIX  415 
LXXXII  418 
LXXXIII  423 
LXXXIV  426 
LXXXV  428 
LXXXVI  433 
LXXXVII  441 
LXXXVIII  451 
XC  453 
XCI  459 
CIII  508 
CIV  509 
CV  513 
CVI  524 
CVII  529 
CVIII  533 
CIX  538 
CX  542 
CXI  555 
CXIII  558 
CXIV  563 
CXV  573 
CXIX  576 
CXX  577 
CXXI  579 
CXXII  581 
CXXIII  583 
CXXIV  586 
CXXV  588 
CXXVI  590 
CXXVII  591 
CXXVIII  596 
CXXIX  603 
CXXXII  609 
CXXXIII  614 
CXXXIV  625 
CXXXV  627 
CXXXVI  631 
CXXXVII  634 
CXXXVIII  637 
CXXXIX  643 
CXLIII  647 
CXLIV  648 
CXLV  653 
CXLVI  656 
CXLVII  659 
CXLVIII  662 
CXLIX  665 
CLI  666 
CLII  669 
CLIII  673 
CLIV  675 
CLV  679 
CLVI  688 
CLVII  690 
CLVIII  700 
CLIX  702 
CLX  704 
CLXI  710 
CLXII  712 
CLXIII  731 
CLXVII  738 
CLXVIII  744 
CLXX  747 
CLXXI  759 
CLXXII  765 
CLXXIII  767 
CLXXIV  780 
CLXXV  783 
CLXXVI  786 
CLXXVII  798 
CLXXVIII  802 
CLXXIX  810 
CLXXX  831 
CLXXXII  835 
CLXXXIII  842 
CLXXXIV  846 
CLXXXV  863 
CLXXXVII  871 
CLXXXIX  891 
899  