Mail server question

[NachT]

I'm not sure if this is even possible, but..

Could I set up a mail server, actually I'm not even sure what it would be called so I'll just keep calling it a mail server until the first person gets here and corrects me

Anyway.. Is it possible, to set up a mail server so that I could make my own email address domain? i.e. could I have myname@customize_this_part_aswell?.com or.whatever

Or a fully customized address that when mail is sent to it, it relays it to a gmail account or something?

I'd want to run the server myself if possible, if there is some software or anything that does it.

I did a google for mail servers, but I got back email clients like outlook express etc, so not sure what they are even called If they exist.

 

[NachT]

So I would download and install a Mail Transfer Agent on my server here, and then just set it up from there?

Do I HAVE to buy a domain? can't I like, download a domain server and set one up xD lol

If I bought one, how would I go about setting the mail thing up. Wouldn't my mail be stored on their servers or?