The easiest way to read on a Linux computer is to use the Online Reader. As far as we know the only compatible browsers that have Linux versions are Firefox and Chrome. Simply install one of these browsers (if not installed already) and you can begin reading straight away.
If you wish to download your ebook unfortunately the solution is slightly more complicated. We do not know of any Linux based ebook reader software that is compatible with Adobe DRM (Adobe Digital Editions does not have a Linux version). So the solution is to use Wine to run the Windows version of Adobe Digital Editions (ADE).
If you want to transfer your ebook from your computer to an ebook reader device this should also be possible, but there is an issue with Wine recognizing USB connections, so this may cause your ebook reader device to not show up under the list of devices in ADE. The solution to this issue can be found here.
Unfortunately because Adobe Digital Editions is not officially released for Linux the support for this solution is limited. But if you do have any issues please check the Help Centre articles for all Windows based Adobe Digital Editions issues as they should be the same. However if you do come across an issue caused by Wine please contact our support team and we will do our best to help. Please be sure to mention you are using Linux and explain the nature of the issue you are having in full.