Go to Email notifications in Settings. You will notice two categories there. The first one is for admins (Root admins can share admin rights to users here) and the second one is for emails not affiliated with your domain.

You can add a new address by unwrapping the Add new email address option below.

Once you do that, a verification email will be sent to the email address. After the recipient clicks on the confirmation link there, notifications will be sent to it per the rules you set up for it.