p-adic L-functions for GL(n)

These are the expanded notes of a mini-course of four lectures by the same title given in the workshop "p-adic aspects of modular forms" held at IISER Pune, in June, 2014. We give a brief introduction of p-adic L-functions attached to certain types of automorphic forms on GL(n) with the specific aim of understanding the p-adic symmetric cube L-function attached to a cusp form on GL(2) over rational numbers.