TITLE: Basic prerequisite (topics) to read current research in Diophantine equation for an independent researcher
QUESTION [10 upvotes]: 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.

REPLY [5 votes]: If I understand correctly, the keywords for the type of number theory you're interested in are "Diophantine approximation" and "transcendental number theory."  Are you aware of Florian Luca's article on Exponential Diophantine Equations?  If not, that might be a good place to start.  You might also like M. Ram Murty and Purusottam Rath's book Transcendental Numbers.
Getting to the research frontier is always a tricky business.  Michel Waldschmidt's Diophantine Approximation on Linear Algebraic Groups will give you a sense of what some of the major open problems in the subject are, but that's a very demanding book.  There undoubtedly exist lower-hanging fruit, but it may be hard to find such fruit without an experienced advisor to guide you.