L-Functions plays a key role in arithmetic. In this talk, we first introduce a new yet geniune non-abelian zeta-Functions for number fields using stability of lattices and a new cohomology. Fundamental properties concerning meromorphic continuation, functional equation and singularities will be established. Moreover, we show that all zeros of rank two zeta lie on the critical line of real part 1/2. Based on all this, we then further give an intrinsic relation of our non-abelian zetas with Epstein type zetas, which then leads to a general definition of non-abelian L functions, using the fundamental work of Langlands on Eisenstein series. At the end of the talk, we will connect this with Arthur's periods and show that classical automorphic L functions are naturally related with what we call the abelian part of our non-abelian L, based on an advanced version of Rankin-Selberg method due to Zagier and Jacquet-Lapid-Rogawski.