I am learning representation theory of Lie groups & Lie algebras from the book by Brian Hall. Unfortunately, this does not discuss infinite dimensional representations. Which books should I study for this when I complete my study of Brian Hall's book?
The following lecture notes of James E. Humphreys on "Representations of Semisimple Lie Algebras in the BGG Category O" might be interesting for you, also including infinite-dimensional representations of finite-dimensional Lie algebras, and much more: http://www.math.umass.edu/~jeh/bgg/main.pdf.
You could try Kac, Victor G. Infinite-dimensional Lie algebras. Third edition. Cambridge University Press, Cambridge, 1990.
Here is a paper by Bernstein and Gelfand that seems pretty influential:
Bernstein, J. N.; Gelʹfand, S. I. Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras. Compositio Math. 41 (1980), no. 2, 245–285.