I've been through a process of installing, uninstalling and reinstalling various versions of Adobe Digital Editions (ADE). There is useful information on which versions of ADE will work on which versions of Wine at the WineHQ website. I found the options below worked for installing ADE on an Ubuntu 14.04LTS system (32-bit).
For all these options, I was able to open some acsm files and download related ebooks. However, only ADE 4.0 allowed me to download ebooks from Google Play that I required. Attempting to download these Google Play ebooks produced a 2038 error on ADE 1.7 and an “E_STREAM_ERROR” on ADE 3.0. I suspect this is due to recent changes in DRM.
INSTALLING ADE 1.7 --- Install Wine and WineTricks (you may need to add the Wine ppa – see https://www.winehq.org/download/ubuntu). Open WineTricks. In the first dialog box take option “Install an app”. On the second dialog box, take option “adobe_diged”. WineTricks will do the rest. Voila! Note that there are numerous older posts in forums that recommend ADE V1.7 over V2.0 and V3.0.
INSTALLING ADE 3.0 --- You'll need Wine and Winetricks for this too (see above for their installation), but the process is a bit more involved. You need to download and install dotnet35sp1 and windowscodecs before running the ADE installation exe. This can be done by opening a terminal and entering this command:
$ winetricks -q dotnet35sp1 windowscodecs
INSTALLING ADE 4.0 --- This option also requires Wine and WineTricks but it requires more advanced versions and the process is even more involved. Nonetheless, there are very comprehensive instructions at: https://appdb.winehq.org/objectManager.php?sClass=version&iId=30928 – follow this link and find the instructions under the comment titled, “How to install ADE-4.xx on ubuntu-14.04 step by step in a console”.