The following list is mostly intended for undergraduates. The recommendations here generally emphasize clarity of exposition over technical detail.

**Algebra and Number Theory**

- Ash and Gross.
*Fearless Symmetry: Exposing the Hidden Patterns of Numbers*. - Carter.
*Visual Group Theory*. - Conway.
*On Quaternions and Octonions*. - Cox.
*Primes of the Form : Fermat, Class Field Theory, and Complex Multiplication*. - Kuga.
*Galois’ Dream: Group Theory and Differential Equations* - Silverman.
*Rational Points on Elliptic Curves*. - Stillwell.
*Naive Lie Theory*.

**Geometry and Topology**

- Adams.
*The Knot Book*. - Mumford, Series, and Wright.
*Indra’s Pearls: The Vision of Felix Klein*. - Needham.
*Visual Complex Analysis*. - Reid, Szendroi.
*Geometry and Topology*. - Richeson.
*Euler’s Gem: The Polyhedron Formula and the Birth of Topology*. - Stillwell.
*The Four Pillars of Geometry*. - Stillwell.
*Geometry of Surfaces*. - Toth.
*Glimpses of Algebra and Geometry*. - Weeks.
*The Shape of Space*.

**Other**

- Aaronson.
*Quantum Computing Since Democritus*. - Doxiadis, Papadimitriou.
*Logicomix: An Epic Search for Truth*. - Gowers (ed).
*The Princeton Companion to Mathematics*. - Lawvere, Schanuel.
*Conceptual Mathematics*. - Mahajan.
*Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving*. - Parikh.
*The Unreal Life of Oscar Zariski*. - Sipser.
*Introduction to the Theory of Computation*. - Stillwell.
*Yearning for the Impossible: The Surprising Truths of Mathematics*. - Wilf.
*generatingfunctionology*.

on January 11, 2017 at 2:23 am |vtakahiroI read Galoia’s dream, when I was a junior high school student.

on December 4, 2014 at 12:35 am |xidalaputaNice list. By the way how do you display math formulas in your blog? I found no button for mathjax plugin on my control panel (and it seems wordpress.com has banned the users freely using plugins)

on December 4, 2014 at 9:16 am |Qiaochu YuanWordPress has some LaTeX support by default.

on November 5, 2014 at 2:54 am |ashwin1729It would be great if you can refine the list!

on February 25, 2014 at 3:10 am |alexRegarding graph theory: I’ve really enjoyed Pearls in Graph Theory (see link if need be: http://www.amazon.com/Pearls-Graph-Theory-Comprehensive-Introduction/dp/0486432327 ). Sadly, both authors passed away.

on December 31, 2013 at 6:39 pm |MASSir this is an excellent list. I have about 9 of these and they are all at about my level of comfort. Ash and Gross’s

Elliptic Talesis a great companion toFearless Symmetrywith a focus on BSD.on September 25, 2013 at 8:55 pm |Mozibur UllahHow about some unorthodox means of instruction like the short video series ‘The Catsters’ by Cheng & co; I couldn’t get a handle on Category Theory until I saw them.

on September 25, 2013 at 8:50 pm |Mozibur UllahHow about Sets for Mathematicians or Conceptual Mathematics?

on September 25, 2013 at 9:35 pm |Qiaochu YuanI haven’t read Sets for Mathematicians but I’m happy to add Conceptual Mathematics to the list. Thanks for the suggestions!

on August 27, 2013 at 1:46 pm |Patrick McLarenI notice you recommend a lot of “soft” books, yet reference “harder” books in your blog posts. What has worked better for you?

on August 27, 2013 at 2:03 pm |Qiaochu YuanI mostly don’t learn from books either way, but part of the motivation behind this list is to counter a tendency towards a “harder = better” mindset when it comes to mathematical resources.

on August 27, 2013 at 3:57 pm |Patrick McLarenIt takes a lot of courage to go against that mindset. I find that the softer books discuss the “why” that I yearn for in the harder books, at difficult spots.

on September 17, 2013 at 8:08 pm |Muhammad FaizanOut of curiosity, what’s your main source of learning/knowledge if not books? I’m guessing that right now you’re probably at the point where most of your knowledge comes from attending lectures and conferences, talking to other mathematicians, and reading papers. But I’m more interested in how you got to this point, especially during your undergrad years, since your pace of learning would be impossible to maintain solely on undergrad math courses. If not primarily books, what sources did you use (and would recommend) to quickly build up a solid foundation of mathematical knowledge pre-grad school?

Thanks!

on September 18, 2013 at 10:11 am |Qiaochu YuanSome combination of papers, Wikipedia, the nLab, math blogs, occasionally books, MathOverflow, and blogging.

on August 14, 2013 at 6:38 am |Vicfredgood recommendations, thanks c:

on August 10, 2013 at 1:09 pm |sdfAm I blind or is there no Serre?!

on March 22, 2015 at 7:07 am |ashwin1729You are not blind and there is no Serre!

on August 2, 2013 at 9:06 am |johnHave you paid for, and read all these booiks?

on July 31, 2013 at 2:24 pm |New page on reading recommendations | Annoying Precision[…] Reading Recommendations […]