Putting out a script runnable by everybody might put too much strain on Springer's servers (and their generosity). I'll give some steps that the motivated can follow instead.

1. Extract a list of all a.btn links from the OP page (382 total).

2. Issue a HEAD request and follow redirects for each link to get the actual page URL (I used curl for this).

3. The page URL contains the book ID. Compare a sample URL's format with its PDF and ePub links. Each page URL can be easily munged into both (sed here).

4. The download pages are captcha-protected, but there's a <noscript> escape hatch in the source. Find it and pass the appropriate data in a POST request to the final file URLs (wget).

A torrent could share the load perhaps

Someone released this a bit ago: https://github.com/alexgand/springer_free_books

Looks like this script is not working anymore. I wanted to try the script when I saw this couple of months back in twitter. And in the process downloaded the whole catalogue.

Perhaps we could all seed your torrent?

I don't torrent, and it's silly to violate copyright on something they're literally offering for free...

Bear in mind that while they're letting you download it for free, Springer doesn't permit redistribution.