Can I use the First or Second Editions of the book? They are much cheaper.

You can, but there is a rather large non-dollar price to be paid. The Third Edition is very extensively revised. There are content changes and all of the numbering is different. Moreover, the First and Second Editions are not supported. There is no error list for example. The Third Edition costs you approximately $50/semester. I don't know what the used other Editions cost, but you can't be saving very much.