TITLE: Recommend books for learning math from elementary school?
QUESTION [10 upvotes]: 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

REPLY [5 votes]: 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:

Algebra
Trigonometry
The Method of Coordinates
Functions and Graphs
Sequences, Combinations, and Limits
Kiselev's Geometry 1 and also 2
Lines and Curves

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:

Calculus of One Variable by Kitchen (if you can find it; otherwise, check out Apostol, Hardy, or Spivak)
Linear Algebra by Berberian
Advanced Calculus by Loomis and Sternberg (very difficult, but awesome!)
Set Theory and Metric Spaces by Kaplansky
Real Analysis by Carothers (Rudin is an easier alternative, but this book is fantastic!)
Elementary Topology by Viro
Elements of Abstract Algebra by Clark (Dummit & Foote is good too)

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