During the last several years, Professor Liu has invited some first-class mathe-maticians from all over the world to deliver lectures and organize seminar for graduate students on number theory in Shandong University. To provide refe-rences for the students, we collect all the lecture notes and latter lectures into some volumes respectively and then make photocopies, in a very simple form
and in a very small number(10). So we build our mathematical library, such that the valuable materials could hand down from today to the tomorrow. All the num-ber theory students are welcome to borrow them, only need a registration. Our mathematical lectures would be extended to a bigger one by replenishing the following wonderful lecture notes in the future.

We would like to repress our cordial thanks to all speakers for their contribution and their great permission to delicate their lecture notes in these volumes. We would also like to thank our students for their industrious work to arrange all the lecture notes.

   Summer School on Number Theory, July, 2006

   Workshop on Number Theory and applications, December, 2005

   Internal Summer School on Analytic Number Theory, August, 2005