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I've learned math long time ago, but I hardly remember anything. I really want to relearn by reading good books, from the ground up. Workbooks didn't really help.

Other posts recommend different books. So a list of best books feels helpful from Pre-algebra to calculus and beyond. Would you be so kind to add which others you recommend. English is not my native language; please excuse typing errors.

Children

  • The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger
  • Alice in Puzzle-Land by Raymond M. Smullyan
  • The Phantom Tollbooth by Norton Juster
  • ...

Beginner

  • What Is Mathematics? An Elementary Approach to Ideas and Methods by Richard Courant
  • Mathematics: Its Content, Methods and Meaning (Dover Books on Mathematics) by A. D. Aleksandrov
  • Mathematics: A very short introduction by Timothy Gowers
  • ...

Basic Math

  • Basic Mathematics by Serge Lang 1998 (high school or college students.)
  • ...

Pre-Algebra

  • Pre-Algebra DeMYSTiFieD by Allan Bluman
  • ...

Algebra

  • Algebra by Israel M. Gelfand 2013
  • A book of Abstract Algebra by Charles Pinter?
  • ...

Algebra II

  • ...

Trigonometry

  • Trigonometry by I.M. Gelfand 2013
  • ...

Pre-Calculus

  • ...

Calculus

  • Calculus by Michael Spivak
  • ...

Problem Solving

  • https://en.wikipedia.org/wiki/Yakov_Perelman#Books
  • How to Solve it by Polya's
  • Techniques in Problem Solving by Steven George Krantz
  • The Art and Craft of Problem Solving by Paul Zeitz
  • How to Prove It: A Structured Approach by Daniel J. Velleman 2006
  • Problem-Solving Strategies (Problem Books in Mathematics) by Arthur Engel
  • Number Theory (Dover Books on Mathematics) by George E. Andrews
  • Some of the books in the Art of Problem Solving series at www.ArtofProblemSolving.com
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    $\begingroup$ If you can handle highschool maths at a decent level, I suggest that masterpiece: How to Prove It. $\endgroup$ – Git Gud Jun 7 '14 at 16:24
  • $\begingroup$ For trigometry i would suggest "Elements of Trignometry" by S.L Loney . Khan academy on youtube will be be helpful . $\endgroup$ – godonichia Nov 22 '14 at 10:19
  • $\begingroup$ At the end of Calculus by Spivak there is a bibliography, in which Spivak suggests books for further reading. If you can get yourself through Spivak and still need more guidance there's a good place to start. $\endgroup$ – Gyu Eun Lee Nov 22 '14 at 11:00
  • $\begingroup$ When you learn from these books, please put them down every now and then and just play with the concepts. Try to anticipate what comes next in a proof, or if you have some tiny question about something you just read, think about it for a while. Have pen and paper ready. Try setting little goals for yourself-- using the tools I have, what interesting fact about numbers can I prove? I have always learned more from doing this than from the actual content of a book. $\endgroup$ – Myridium Oct 15 '16 at 4:56
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well I don't know about the books but you should try www.khanacademy.com while reading those books, to better grasp all the concepts :)

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    $\begingroup$ Thank you. After reading your comment I bought all Dannica McKeller books and I visit www.khanacademy.com while reading her books. I have finished all her books except one, her latest one. And Khan Academy helps me better grasp the concepts very well. Thank you for your advice. $\endgroup$ – Abdabdi Jan 4 '15 at 16:04
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For "highschool level" you might try the Art of Problem Solving books (they have materials for students in elementary school now as well if those are too advanced). I also recommend the following books:

If you're interested in more advanced problem solving/olympiad material, check out this page, and this page. You needn't read all of this stuff, but pick what looks good and what you have time for.

For more advanced stuff (what most consider undergraduate studies), you might check out the following to get started:

These will get you started. I tried to choose books that are challenging, cheap/free, and have lots of problems.

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For precalculus (and trigonometry, since it's included in precalculus) I recommend Precalculus: Graphs and Models A Right Trangle Approch 5th Edition by Bittinger, Beecher, Ellenbogen, Penna. This book includes lots of real life application problems throughout the chapters.

For calculus I recommend Calculus by James Stewart. It's used for mathematics education all over the world, and speaking from my own experience it's a very good book. It includes a lot of problems to practice with, and after each chapter a real life application problem. There are two versions: a single variable version, a multivariable version and a version that includes both. You have to begin with single variable calculus, so make sure you buy the right one.

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For a good understanding of basic algebra, I recommend you study the book "College Algebra" (2014) by Paliogiannis.

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