If one needs to use tools from classical invariant theory or elimination theory then some books that come to mind are:

• Grace and Young "The Algebra of Invariants", 1903.

• Elliott "An Introduction to The Algebra of Quantics",

• Salmon "Lessons Introductory to The Modern Higher Algebra", 1876.

• Faa di Bruno "Théorie Des Formes Binaires", 1876.

• Faa di Bruno "Théorie Générale de l'Elimination", 1859.

and there are quite a few more.

If one needs to use tools from classical invariant theory or elimination theory then some books that come to mind are:

• Grace and Young "The Algebra of Invariants", 1903.

• Elliott "An Introduction to The Algebra of Quantics",

• Salmon "Lessons Introductory to The Modern Higher Algebra", 1876.

• Faa di Bruno "Théorie Des Formes Binaires", 1876.

• Faa di Bruno "Théorie Générale de l'Elimination", 1859.

and there are quite a few more.

For Salmon's book, the 4th edition of 1885 might be best. Indeed, as I learned from a paper by Macauley, it has a discussion (on p. 87) of Cayley's very general formula for the multivariate resultant as the determinant of a complex (see the book by Gelfand, Kapranov and Zelevinsky for a modern account and a reprint of Cayley's paper).

If one needs to use tools from classical invariant theory or elimination theory then some books that come to mind are:

• Grace and Young "The Algebra of Invariants"

• Elliott "An Introduction to The Algebra of Quantics"

• Salmon "Lessons Introductory to The Modern Higher Algebra"

• Faa di Bruno "Théorie Des Formes Binaires"

• Faa di Bruno "Théorie Générale de l'Elimination"

and there are quite a few more.

If one needs to use tools from classical invariant theory or elimination theory then some books that come to mind are:

• Grace and Young "The Algebra of Invariants", 1903.

• Elliott "An Introduction to The Algebra of Quantics",

 

• Salmon "Lessons Introductory to The Modern Higher Algebra", 1876.

• Faa di Bruno "Théorie Des Formes Binaires", 1876.

• Faa di Bruno "Théorie Générale de l'Elimination", 1859.

and there are quite a few more.