We study automorphic L-functions for GL(2) over a global eld (e.g., those attached to elliptic curves). In the case of the rational number eld, the Gross-Zagier formula expresses the rst derivative in terms of the height of Heegner point on a modular curve. In the case of function elds, in a joint work with Zhiwei Yun, we found a family of algebraic cycles on the moduli of rank two Drinfeld Shtukas, and we prove that their intersection numbers give higher order derivatives of L-function. The lectures will review the backgrounds and we will present the main ingredients in the proof. If time permits, we also discuss several constructions of algebraic cycles on Shimura varieties over number elds.