Well.......yes you could save each individual e-mail one at a time locally, but depending on the e-mail client that could be as a text file or as an e-mail file which still needs the same client software to read....
you're using AOL, so I think the only way to do it would be to download the e-mails using an IMAP client and then save them from there. From memory the AOL client does not allow local text format saves
Even if you do save them as text files, you'll lose any formatting, attachments and images. Also searching them will become a lot harder