  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.
