I have completed studying Galois theory, Fermat's Last Theorem for Regular prime and some number theoretic complex analysis (prime number theorem), and basic linear forms in logarithm.

What else should I complete reading to be eligible to read contemporary literature in Diophantine Equation (Exponential) ?

My graduation was in engineering, so I am from non-math (I mean serious math!) background, and I am not going to a university in near future, but wish to conduct research as an independent researcher.

There might be a lack of specification in my question, so if possible, adjust your answer according to that, also feel free to edit.

Rational Points on Varietiesby the irrepressible Bjorn Poonen) contains a lot of the prerequisites you would need in case you go the algebro-geometric route: www-math.mit.edu/~poonen/papers/Qpoints.pdf $\endgroup$ – RP_ Aug 8 at 21:01via longissima). The "pay-off" of your studies (meaning concrete results and papers of your own) would probably be greater if you wouldn't concentrate exclusively on all that high-falutin stuff, and set your sights more on analytic number theory, additive combinatorics, recreational problem solving... There is always a severe danger of involving yourself in massive propaedeutic studies, without the slightest guarantee of the possibility of contributing something of your own. Just my two cents... $\endgroup$ – RP_ Aug 8 at 21:09