Not Adobe DRM files. Amazon sells the Kindle cheap so it can force up sales of its properietry eBooks.
It should read non-DRM .epub files, or you can convert them to Kindle format using a program such as Calibre.
I must disagree since lots of FREE books are available in Kindle format with Overdrive download from my county library. I find Adobe guilty or arrogance and greed more so than Amazon.
Our library (Hampshire, UK) initially only supported Adobe DRM format for loans.
They now seem to support Overdrive Read as well, I think that is for reading direct from the browser?
No sign of any Kindle support.
It seems lots of US public libraries support Kindle, but not many UK ones. Where are you?
My main concern with Adobe is that they provide this relatively 'open' infrastructure,
but their support for it is absolutely atrocious; replacing second-rate ADE 1.7.2 with third-rate (fourth-rate?) ADE 2.0 and 2.0.1.
I'm in the US. My local library support Kindle with Overdrive downloads.