I have completed calculus courses but I have dropped out real analysis. However, I have basic knowledge of analysis and algebra to some extent like I know about group theory and about basic real analysis. I have also completed differential equations and basic linear algebra course.
Is it possible for me to start number theory as a self study at home without much difficulty. If yes, how? If no, Why?
I basically am aiming to read Ramanujan's Notebooks successfully. Thanks
It is possible to study Number Theory (admittedly, at a rather low level) without any university-level mathematics at all. I picked up Albert Beiler's book, Recreations in the Theory of Numbers, when I was 12 and had a blast with it.
Now if you like your mathematics with theorems and proofs, you could still pick up Hardy and Wright, An Introduction to the Theory of Numbers, or Niven, Zuckerman, and Montgomery, An Introduction to the Theory of Numbers, and get through most of the book without much university-level math.
Getting to the level of Ramanujan's Notebooks, well, I'm not sure what you'd need for that. But you'll certainly need large chunks of what's in H & W, or in N, Z & M, so you might as well get started with one of those.