Based on biesta's comment:

# This is a detailed 'howto'-document,
# how to install ADE-4.xx on *ubuntu-14.04* step by step in a console.
# Prerequisite: (x)ubuntu-14.04, system-update if required.
#
# Install the winbind package, if not yet done:

$ sudo apt-get install winbind

# Check if wine (actual version) is available:

$ wine --version

# response should be 1.7.33 (or newer?)
# install wine if required:

$ sudo add-apt-repository ppa:ubuntu-wine/ppa
$ sudo apt-get update
$ sudo apt-get install wine1.7

# To accept the License agreement, press Tab + Enter.
# Check if winetricks (actual version) is available:

$ winetricks -V

# ...response should be 20141125 (or newer?)
# install winetricks if required:

$ wget winetricks.googlecode.com/svn/trunk/src/winetricks
$ sudo cp -f winetricks /usr/bin
$ sudo cp -f winetricks /usr/bin/X11
$ sudo chmod 555 /usr/bin/winetricks
$ sudo chmod 555 /usr/bin/X11/winetricks

# install WINEPREFIX + 32bit-environment:

$ export WINEPREFIX=~/wine32a # or similar, e.g. ~/.wine32b
$ WINEARCH=win32 winecfg

# ****** IMPORTANT: ******
# The winecfg-command opens a GUI-window,
# with a drop-down element labelled "Windows Versions" (or similar).
# Default position is "Windows XP".
# Do NOT change this or anything else in the GUI, or the installation will fail.

$ winetricks -q corefonts dotnet40

# download + install ADE-4.xx (actual version?)
# im your browser: from
# www.adobe.com/de/solutions/ebook/digital-editions/download.html

$ wine ~/Downloads/ADE_4.0_Installer.exe