saving email to personal computer

How do I get eM Client to save my emails onto my computer?  Right now I have to be connected to the Internet to see even my old emails.

Hello David,
if your account is an IMAP one, go to Tools>Accounts and under your email account, click the IMAP tab and check the option to ‘Download messages for offline use’.
This will save the whole message onto your computer to access offline. eM Client only saves Mail Headers for IMAP accounts’ emails by default unless you check this option to save space and make the application faster (and downloads the whole message only once you read it).

Regards,
Olivia

Will dragging a message to a local folder save it as well?

Yes