There are two dominant protocols on the Internet for reading/downloading email from servers (at least if we do not count web based reading), and they are IMAP and POP3. The former being the slightly more modern alternative. curl supports both.
To list message numbers and sizes:
curl pop3://mail.example.com/
To download message 1:
curl pop3://mail.example.com/1
To delete message 1:
curl --request DELE pop3://mail.example.com/1
Get the mail using the UID 57 from mailbox 'stuff':
curl imap://server.example.com/stuff;UID=57
Instead, get the mail with index 57 from the mailbox 'fun':
curl imap://server.example.com/fun;MAILINDEX=57
List the mails in the mailbox 'boring':
curl imap://server.example.com/boring
List the mails in the mailbox 'boring' and provide user and password:
curl imap://server.example.com/boring -u user:password
POP3 and IMAP can both be done over a secure connection and both can be done
using either explicit or implicit TLS. The "explicit" method is probably the
most common approach and it means that the client connects to the server using
an insecure connection and upgrades it to TLS as it goes, using the
STARTTLS command. You tell curl to attempt this with --ssl or if you want
to insist on a secure connection you use --ssl-reqd. Like this:
curl pop3://mail.example.com/ --ssl-reqd
or
curl --ssl imap://mail.example.com/inbox
"Implicit" SSL means that the connection gets secured already at first
connect, which you make curl attempt by specifying a scheme in the URL that
uses SSL. In this case either pop3s:// or imaps://. For such connections,
curl insists on connecting and negotiating a TLS connection already from the
start, or it fails its operation.
The previous explicit examples done with implicit SSL:
curl pop3s://mail.example.com/
or
curl imaps://mail.example.com/inbox