The new edition for Mathematica 8 is out. (Clicking on an image will take you to the Wolfram bookstore.)
Version ≤ 9 users: Here's the notebook of convenient initialization code for the multivariable manual. Copy & paste its contents into your init.m file. You can open your init.m file by entering the following command in Mathematica.
Version 10 users: Here is the new notebook of initialization code. (See above for instructions.) This is the same as the old one, except the functions Grad, Curl, Div, and Laplacian have been deleted, since they are now built-in functions in Mathematica 10 (and thus their definitions generate "symbol protected" warnings). If you already have the old code, you can just delete them from your init.m file. The new built-in versions of Grad, Curl, Div, and Laplacian appear to work in the same way, so no further changes should be needed, but you'll want to avoid attempting to define them yourself. (However, no harm will be done if you do.)
If you're using the old 4e version of the multivariable manual, you need the Vectors package. You can get it by clicking here and then saving the file as Vectors.m. Once you do that, put the file in Mathematica's Applications folder. (To learn where that is, enter $InstallationDirectory in Mathematica.)
An alternative to installing the package is to load it remotely by entering the following command:
That takes the place of either of <<Vectors` or Needs["Vectors`"]. Amazing, huh?