This is a really good introduction to vim. It is better to think of it as a grammar to manipulate text.

A few additional things that have saved me keystrokes...

replace mode (R)

insert normal mode (<c-o>)

paste from a register in insert mode (<c-r>reg)

expression register (=)

clipboard and active selection registers (+, * respectively)

command ranges (e.g. 10,+5s/foo/bar/g)

miscellaneous commands (:global, :argdo, :normal, etc...)