Good math books?

Okay here's the story,
I always loved maths, but for some reasons i dropped out of school.
Now at 22 i want to start studying maths again, but i do not know where to start from..

tl;rd suggest me some books that cover the basics and the advanced stuff of mathematics, algebra and geometry.

7 here, I say go for it regardless of what others say (which sounds like what you've already decided, great!).

I'm looking through my old textbooks to give you some good recommendations as per your request.  I really love my Calc book by Larson, Hostetler and Edwards (just titled 'Calculus').  It's a solid book all around: covers all of Caclulus (even goes into multivariable and diffeq a little), has complete proofs for everything, most importantly it is easy to read and gives refershers for lots of things preceeding Caclulus.  If you get frustrated with the difficulty of learning math on your own, try this book.

As mentioned, "The Principles Of Mathematical Analysis" by Rudin is the best book for Analysis, hands down.  The area of math called 'Analysis' is basically everything which directly follows (and encompasses) Calculus.  While reading Rudin keep in mind his style is to prove things *very* concisely, which can be intimidating.  Logically one could do Rudin right after (or instead of) Calculus, but realistically one has to work their way up to this difficulty.

For Algebra I like the book by Artin.  There aren't any prerequisites for Algebra besides knowing what a set is and a little Linear Algebra, and he does cover I think all of what you need from Linear Algebra in the first chapter.

Don't be too intimidated by the thought that there are tricks which aren't taught in textbooks.  You can pick up lots of those tricks slowly anyways, and even so these tricks are generally not teaching you anything too important.  What's in the meat of the textbooks is the most important part. 

The hardest part for someone just starting to study mathematics is learning how to *prove* things rigorously, which is something that is not emphasized in high school mathematics.  It is vital that you try to understand every proof when you read a textbook.  It should be your aim to eventually understand all the proofs.  Even better you would like to be able to commit to memory the general idea of each proof so that from the general idea you can reconstruct the entire proof by hand.

A final thought is that many textbooks have exercise solutions available online written up by students.  I know you can find most of the solutions to Rudin online, for example.