Each device supports different formats.
Nook, Sony, Kobo and more: These eReaders will work with the widest variety of downloadable library eBooks. PDFs may be easily transferred to them, and they are compatible with Adobe Digital Editions. If you own one of these eReaders, you shouldn't have many problems getting content onto your device.
Amazon Kindle: Unfortunately, the Kindle is not compatible with Adobe Digital Editions. However, you can still transfer PDFs to the eReader, so there are many library eBooks to read on this device.
iPad, iPhone and iPod Touch: Compared to most eReaders, these devices provide a much better reading experience online. They are also excellent for reading PDFs. You can also download an app like Bluefire (http://itunes.apple.com/us/app/bluefire-reader/id394275498?mt=8) that is compatible with Adobe Digital Editions.
Android phones and tablets: Compared to most eReaders, these devices provide a much better reading experience online. They are also excellent for reading PDFs. You can also download an app like Aldiko (https://market.android.com/details?id=com.aldiko.android&feature=search_result) that is compatible with Adobe Digital Editions.
Windows Surface: The Windows Surface Pro will allow you to read any of our books online or offline. Unfortunately, with Surface RT has some limitations. Adobe does not currently offer Adobe Digital Editions for the Windows RT operating system, and there are not currently any compatible apps. So, if you have a Surface RT, you will only be able to read DRM-free books offline.
While many eBook formats exist, EPUB is emerging as the industry standard, readable on most major tablets and eReaders except the Kindle (which uses Amazon's own proprietary format). The newest version of EPUB allows for compatibility across a wide variety of devices and provides publishers with formatting control, interactivity, and accessibility features.
See the EPUB site for more.