Brian Conrad said, 'Algebraic group is a very interesting mixture of group theory and algebraic geometry. Over finite fields it explains virtually all finite simple groups, over number fields it illuminates many important problems concerning quadratic forms and modular forms and beyond, over the real numbers it clarifies the theory of Lie groups and so on'.

In this course, we will study basic knowledge of algebraic groups. Our ultimate goal is to understand the structure and the classification of reductive groups and semisimple algebraic groups.

Basic background of algebraic geometry is recommended.

Attendance and Homework. You will get F if you miss more than 5 classes.

1. J. Milne gave a course about the topic. The lecture note was available on his webpage but currently was merged into several other lecture notes (total pages are around 1,000) given at http://jmilne.org/math/CourseNotes/ala.html.
I will post his initial lecture note written in 2005 at LMS.

2. Brian Conrad gave a course about the topic. His lecture note as well as syllabus are available at
http://virtualmath1.stanford.edu/~conrad/252Page/
and
http://virtualmath1.stanford.edu/~conrad/249BW16Page/

3. Jiu-Kang Yu gave a course about the topic. I will follow some of his note (which is not available on the internet).

4. Springer's Linear Algebraic Groups. This book includes almost necessary theorems about the topic.

More references will be updated during the lecture (and LMS) if necessary.