In this mini-course our goal is to explain the recent approach by Paul Nelson

to get subconvexity bound for L-function on higher rank groups like����or GL��. We

will give some numerical evidence why this approach can give nontrivial bound. For

this goal we shall also review some notions and tools in the theory of automorphic

forms. The main topics include

(1) Local fields, adele, idele

(2) Basics about groups

(3) From modular forms to automorphic forms and representations

(4) Classification and examples of local representations

(5) Spectral decomposition and period integrals

(6) Relative trace formula

(7) Application to subconvexity bound