Before you settle down to enjoy this nine-disc set, two grumbles have to be dealt with.
The first is that any real fan of the Alien series (or early adopter of DVD as a home entertainment medium) already owns an excellent five-disc set of the same films that came out a scant two-and-a-half years ago. The second is the sheer embarrassment of asking in a shop for something called a "quadrilogy" - the unwieldy coinage (after all, if you replace the "tri" in "trilogy" with "quad" you should get "quadlogy") is presumably used because they tried the more dignified Alien Quartet last time.
However, the bad news for your pocket is that this really is an essential purchase, and is liable to serve as a benchmark for meaty DVD releases of important franchise sets from now on. With Ridley Scottís original 1979 Alien freshly spruced-up and tweaked for theatrical re-release, it would have been easy to let the old, previously accepted version disappear (try to see the original Star Wars, for instance).
This set presents each of the four instalments twice: in the "theatrical cuts" as well as some form of director-authorised (or not) extended or alternative edition.
Alien appears in its 1979 and 2003 cuts (the newer version puts back Tom Skerritt's cocooning and includes a nice cat-fight between the female leads, but trims some meaningful or terrified looks).
James Cameron's Aliens is here in its action-packed 1986 version and the more fleshed-out Director's Cut (the longer one establishes Ripley's first name, Ellen).
David Fincher's Alien3 comes as the little-liked (but interesting) release version and a different 139-minute cut that may not be much more enjoyable, but is certainly more understandable (you'll realise why Paul McGann is so prominently billed, as his alien-worshipping subplot is restored and there's a different host animal as the alien erupts from a steer rather than a dog).
Finally, Jean-Pierre Jeunet's Alien: Resurrection is included as the regular version and one topped-and-tailed with half-finished but nice-to-see sequences (a witty opening with a bug in close-up that seems like an alien, and a Planet Of The Apes-style finish).