Much of the material for today has been taken from ``Some examples of problem solving by using the symbolic viewpoint when dealing with polynomial systems of equations'' by Laureano González-Vega, which I have in technical report form (from the University of Cantabria). The full reference is
Laureano Gonzalez-Vega, ``Some Examples of Problem Solving by using the Symbolic Viewpoint when dealing with Polynomial Systems of Equations'', in Computer Algebra in Science and Engineering, J. Fleischer, J. Grabmeier, F. W. Hehl, W. Küchlin, eds World Scientific, 1995, pp. 102--116.
Additional references include the wonderful book Ideals, Varieties, and Algorithms, by Cox, Little and O'Shea. It is in the library here at UWO, and has become one of my favourite texts. It is clear, coherent, deep and refreshing, as well as containing a lot of useful information. In particular, it has all the detailed proofs that I will be leaving out of these lectures.
More pedestrian but perhaps as useful is the book
Algorithms for Computer Algebra
by Geddes, Czapor, and Labahn. Chapter 10 is on Gröbner bases. Stephen Czapor
grobner package in Maple.