There are two possibilities.
1) ~~~
You can keep the old Adobe account, but change the email associated with it.
That is what you need to do if you have bought books that you want to continue to read.
To do that, go to the Adobe web page and sign in using your old email.
Then go to My Adobe (top right) and My Adobe ID (near top left under My Information).
There you can change the Adobe ID associated with the account, and hit 'Save Changes'.
This won't change the authorization of the PC to the account.
It might still give the old email for a time if you query authorization;
but it is the account that is important, not the email it is currently registered to.
To be extra sure, you can deregister [ctrl-shift-D (cmd-shift-D on Mac)] and reregister, as below.
The old email is just an identifier, it doesn't matter that it is no long valid.
Unless you have forgotten the password, in which case you won't be able to use standard password recovery.
If you need the old account and have forgotten the passsword and no longer have access to the email account,
you must contact Adobe to get it all setup again.
2) ~~~~~
You can create a new Adobe account for your new email.
This may be easier if you only use library books and don't need access to any DRM books registered to the old account;
especially if you have forgotten your password.
For a new account, once you have signed up for the new account at the Adobe website,
use ctrl-shift-D (cmd-shift-D on Mac) to ADE (Digital Editions) to remove the old registration.
Then go to menu/Help/Authorize Computer (Library/Authorize Computer on the older more reliable v1.7.2) and authorize with your new ID.