Abstract: In the first part , I will introduce the classical Siegel-Weil formula, which expresses an Eisenstein series as a weighted average of theta series associated with lattices in a genus. I will then explore how to interpret it within the framework of the theta lifts.

In the second part, I will discuss the Rallis inner product formula, which relates the Petersson inner product of theta lifts to the special value of an L-function. I will explain how this result is established using a see-saw argument and the Siegel-Weil formula.