I've always been bad at math, partly because I've never cared, partly because none of my highschool teachers have never tried to instill in us an interest in math. Obviously I know how to add, subtract, multiply and divide. But beyond that my knowledge becomes fuzzy. It's something I've always had a complex about.

What's a good way to start, considering that what I want is not necessarily to solve specific problems, but to understand mathematics and the logic behind it?

For what it's worth, I have always learned best by first delimiting the boundaries of a field (where it starts, where it ends and what it encompasses).