ADE 2.0.1 Linux
WARNING. THESE PROCEDURES HAVE NOT YET BEEN TESTED OTHER THAN IN THE COURSE OF DOCUMENTING THEM. USE AT YOUR OWN RISK. THIS WARNING WILL BE REMOVED WHEN THE PROCEDURES HAVE BEEN VERIFIED TO WORK BY OTHERS. PLEASE POST YOUR FEEDBACK.
UPDATE: I have myself followed these procedures to install ADE 2.0.1 on a notebook machine running Manjaro, an Arch derivative, which preveiously did not have wine installed at all. I also have one independent report of success.
With Version 1.7.2 of ADE no longer working for Overdrive and Google Books it has been necessary for users of this venerable version to upgrade. The preferred version to upgrade to for those of us who wish to stick to versions that don't support Adobe's new DRM scheme is 2.0.1. Unfortunately, unlike version 1.7.2 it is not a simple matter of using Winetricks, though perhaps this will come later. However, many Linux users seem to be having difficulty in getting this version to run in Wine. Fortunately, it can be done.
My thanks to the contributors on the various MobileRead threads who have posted their experiences and workarounds.
These procedures will create and install ADE into a new 32 bit wine prefix at $HOME/.adewine. You can damage your existing wine installation. Follow this at your own risk.
You will be working in a terminal and one of the first steps is to set an environmental variable to point to the ade wine prefix. You should run all commands from this terminal. Using another terminal will apply the commands to your default wineprefix unless specified otherwise in that terminal.
You should have Wine and Winetricks installed and functioning.
 Files to Download
Open a terminal window.
 Step 1
We will now create the new WINEPREFIX for installation. At the command prompt run
WINEPREFIX=~/.adewine WINEARCH=win32 wineboot
 Step 2
Now we will set the environment so that any relevant command run from this terminal will use the new wineprefix. Run:
 Step 3
Now we will use Winetricks to install some needed files. There is a Winetricks verb also for the dotnet framework SP1. However, this should be avoided. as it downloads earlier versions which seem to create a conflict. We will install the framework later using the installer file downloaded earlier. Run:
winetricks -q windowscodecs && winetricks -q corefonts
 Step 4
This step is optional bur recommended. The new wineprefix has default settings and the windows produced may well be too small for comfortable reading.
A window will appear. Select the graphics tab and you should see a slider to adjust the dpi. Adjust this to a more comfortable setting. It is not necessary to make any other adjustements at this point.
 Step 5
Install the dotnet framework file you downloaded earlier. Assuming the file is stored in ~/Downloads the command would be:
This will take some time to download files and complete. For some reason the download seems to be very slow even on a fast connection. Be patient. Go have a coffee.
 Step 6
You should now have the dotnet framework installed. It is finally time to install ADE 2.0.1 which you downloaded earlier. Once again assuming it is in ~/Downloads the command would be:
This should actually install very quickly, unlike the dotnet framework in the preceding step.
If all has gone well you should now have a working installation of ADE 2.0.1. If it offers to migrate books I recommend refusal, though I didn't personally try.
 Winetricks Version
This procedure failed to install for a user running Linux Mint with winetricks 20140302 and wine-1.6.2. The procedure was developed using winetricks 20160628 and wine-2.0.
The user only got as far as installing corefonts which failed. The log showed that the older version of winetricks was trying to download the corefonts from an obsolete link.
The easiest solution would of course be to update winetricks to the later version. Another possible solution would be to manually download the 10 corefonts and install them.