The Classic Math Textbooks

There may not seem to be anything special about the math textbook you use, but there are actually some texts considered by the mathematical community to be classics.  They're usually considered exceptional because of how clearly or thoroughly they're written, or because they were authored by
the mathematicians themselves who were fundamental in starting that particular field of math. 

Math textbooks definitely are written in a style that reflects the historical time period.  Math vocab words come in and out of style, and proof methods or the use (or lack!) of figures in the text changes over the years.  Some of the older texts are hard to learn from at first, and it might be helpful to use them as a second textbook for a particular math field.  Others have been revised and updated several times and are more readable.

"Classic" is a subjective term that, in this list, is mixed a little with "recommended."  Opinion is definitely involved when making "classic" lists!
Showing 13 items
AuthorTextbook TitleDescriptionLink to AmazonRelated linkYear (most recent edition)Year (first edition)
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AuthorTextbook TitleDescriptionLink to AmazonRelated linkYear (most recent edition)Year (first edition)
Artin Algebra Famous author. More personal than Lang or Dummit & Foote, but covers less material. Makes interesting connections between different topics. Artin, 1st Ed Artin on Wikipedia 2010 1991 
Dummit & Foote Abstract Algebra Dense, graduate level, 933 pages, more than a full graduate year of algebra content. Dummit & Foote, 3rd Ed  2003  
Euclid Elements No math textbook list is complete without Euclid's Elements, which was "The Book" in math for 2000 years. Many versions on Amazon Free download  300 B.C. 
Folland Introduction to Partial Differential Equations  On Amazon  1995  
Guckenheimer & Holmes Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields Authors just won the Steele Prize for this text. On Amazon  1983  
Hardy & Wright An Introduction to the Theory of Numbers Andrew Wiles just spearheaded a revised 6th edition in 2008 after five classic editions of this text from 1938-1979. The 6th edition finally includes an index! Does not include exercises. On Amazon About this text on Wikipedia 2008 1938 
Lang Algebra Famous author. Very dense, non-narrative. Lang, 3rd Ed. Lang on Wikipedia 2002  
Lang Differentiable Manifolds A dense foundational classic which includes the infinite dimensional case. Lang also has a Springer text by a similar title. On Amazon  1988  
Munkres Topology Student-friendly. Covers set theory, point-set topology, and introductory algebraic topology. Munkres, 2nd Edition  2000 1975 
Pinter A Book of Abstract Algebra Easy, readable, friendly guide. Great first text to start. Pinter, 2nd Ed  1990 1982 
Royden Real Analysis  Royden, 4th Edition  2010  
Rudin Principles of Mathematical Analysis "The Bible of classical analysis," difficult as a first text Rudin, 3rd Ed  1976  
Spivak Calculus "The" calculus book, but not used widely in the classroom. Spivak, 4th Ed  2008  
Showing 13 items