This course aims to introduce students with a background in basic algebra, commutative algebra, and topology---but not necessarily one in algebraic geometry---to the subject of linear algebraic groups. The topics covered will include: Jordan decomposition, tori, the Lie algebra of an algebraic group, quotients, and parabolic and Borel subgroups. We will stop short of classifying reductive algebraic groups over algebraically closed fields by means of their root data.
The text book for the course is:
Linear Algebraic Groups, Second Edition (1998) by
T. A. Springer
Videos of lectures are
here.
Note added after completion of the course:
The syllabus for the course as described above turned out to be too
ambitious. We ended up only as far as section 4.3 of the text.