I want to learn more about the Euler-Mascheroni constant, $\gamma$ and do research on a problem related to it. The problem does not necessarily has to be the question of rationality/irrationality of $\gamma$ but rather can be a different one that is yet unanswered. But I am interested only in pure/Theoretical questions regarding $\gamma$ rather than computational or applied ones.
But in general, which branch of mathematics studies this constant and its characteristics? Is it Number Theory(or a specific sub-branch of it)? But I have not studied Number Theory since there is no such course in my college.
Can someone tell me which branch of Mathematics studies it and what could be some good books to get started and reach up to an intermediate/advanced level so that I can carry out some real research in this field.