### Material for Math 207C Spring 2010.

The following consists of the almost legible, very rough lecture notes for
the first lecture.

**The first lecture.**

In the following material the reference [GW] is to the link after
the next one. The reference to [S] is to Shafarevich Basic Algebraic
Geometry I, Second Edition, Springer-Verlag, Berlin,1994.

It is a fix with some additions to the original version (note the
date). The major changes are from p.9 on.

**Basic Algebraic
Geometry (Revised 4/13/10)**

**The appendix on algebraic geometry in
Goodman-Wallach, Symmetry, represenations and invariants,**

Below is a link to the basic material we will be using on
Algebraic and Lie Groups.

** Material on Algebraic and
Lie groups.**

Most of the material that is unproved in this link can be found in

**The first chapter in GW.**

**The appendix on Manifolds in GW.**

** Material on Basic geometric
invariant theory.**