Book Supplement to Griffth and Harris Principle in Algebraic Geometry There is a Chapter 0 (Foundation Level) in Principle in Algebraic Geometry. What are those good book supplement to this chapter ?

Huybrechts' _Complex Geometry: An Introduction_ is a good book to supplement chapters $0$ and $1$ of Griffiths and Harris. It covers pretty much the same material, but often covered in more detail. In particular, section $1.2$ has a nice discussion of the multilinear algebra that you need.