A lot of people have mentioned Keith Devlin's book "Introduction to Mathematical Thinking" by Keith Devlin but for me his other book "Mathematics: The Science of Patterns" was something that really had a huge impact on me just to put mathematics in perspective. Probably has something to do with my own personal character and education but I needed that perspective before I could take the next step. Then the "Introduction to Mathematical Thinking" is a great following read. So it depends where you are.