Hi SaudiSue,
Yes you can - I've done it with my Reader (I use my desktop at home, and a laptop if I'm away).
You just need to install the Reader Library software on both computers - and when you authorise the computer for copyrighted content (the prompt for this usually appears automatically when you first try and transfer coprighted eBooks), then just make sure that you use the same Adobe ID and password that you used for your first computrer (and Reader). After that you can use whichever computer you like with your Reader!
