Where to start reading on logic?

I am a medical graduate who is wondering where to start reading on logic. I only have high school mathematics knowledge - was good at it - but out of touch with it for a while now. Recently I have read a book on the history of philosophy, and got interested in analytic philosophy. I'm familiar with some of continental philosophy, and have read some 19th century philosophers, but analytic philosophy seems to demand knowledge in logic and mathematics. I remember reading a mathematics book in high school which I believe explained the origins of calculus in logic (with axioms and propositions), and that was not a hard (actually quite exhilarating) read. I want to know what the likes of Russell, Frege, and Quine were about, and for that I sense that I need some introductory course on logic and mathematics. Where can I get/read this? I have a few years of time at my hand. If anyone can guide what books/courses I can look forward to, it would be helpful.