Thanks in advance.
Maybe start with something like: Courant & Robbins, WHAT IS
MATHEMATICS? [recently Courant, Robbins & Stewart]
Then when you have a general idea choose more specialized books.
I'll heartily second that suggestion. Courant and
Robbins' book has withstood the test of time quite
remarkably well, and nothing else that I have seen
comes close to its breadth of coverage and its
readability.
--
One book that I am particularly fond of, which will give you some
insight into the "flavor" of advanced math (along with the important
tools to go further, should you find you have the stomach for it) is
"A transition to Advancd Mathematics" by Smith, Eggen, and St. Andre.
HTH,
M