You can't download and install ADE on the tablet.
You can install an app such as Bluefire; which allows the reading of DRM eBooks.
For non-DRM books, just copy them to the tablet and open with Bluefire.
For DRM books:
For library books, there is a an Overdrive app for the tablet.
This will let you borrow, download and read books all from the same app.
Several vendors have their own app that lets you buy, download and read directly to the tablet.