Hi, I've got a Kindle and my adobe digital editions doesn't recognize it. I have allready authorized my pc, what can I do?
Kindles do not support files supported by Adobe Digital Editions. Kindle supports Amazon's own file format and I belive mobi and maybe prc. My library supports downloading of lended books direct from the Amazon website.
Unfortunately as Michael says, Amazon intentionally block many possible uses of the Kindle; the price is low because they hope you will buy books from them.
For example, this makes it unusable for UK library books.
Most other eReaders are more open: some (such as Nook) make it easier to get books from a particular supplier, but don't completely tie you in the way Kindle does.
For non-DRM books you can use the Calibre software to do format conversion and export to Kindle.