You can continue to use the same Adobe ID even though the email address is no longer in use.
That way you will still be able to read all your old books.
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You can change the email address associated with the ID without changing the ID itself.
Sign in to your adobe account on the web using your old email address and old adobe password (NOT you old email password)
and go to the page https://www.adobe.com/uk/account/account-information.html#myadobeid
Change the email address for your AdobeID on that page to your new email.
You will need to verify the new email address by responding to the auto-response from that change.
The Adobe ID will effectively be exactly the same as before with access to all the old books, just associated with your new email address.
Your Adobe password will not change (unless you choose to change it as well as changing the email).
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If you have already set up a new AdobeID associated with your new email and want to keep your old books,
you will need to discard that new AdobeID as you won't be able to read any of your old books with it.
Also, in that case it may not allow you to change the email address associated with the old id.
You may have to keep the old email address as the name for your AdobeID, but set up your new email address in the 'Alternate email address' field.
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If you have already used a new AdobeID with ADE you will need to clear any association with a new ID on your copy of ADE.
Hit ctrl-shift-D (cmd-shift-D on Mac) to clear the association, restart ADE, and then reregister with the original ID.