Now, little bit about MAPI.
According to wikipedia MAPI is designed to be independent of the protocol, it is usually used with MAPI/RPC, the proprietary protocol that Microsoft Outlook uses to communicate with Microsoft Exchange. So, I read this like MAPI is a protocol.
To use MAPI you will need MS Outlook MS Exchange or MS Exchange client, which you can download from here, installed on machine.
There are two kind of MAPI, simple MAPI and extended MAPI.
According to Microsoft most of functions of simple MAPI are deprecated, so I focus here on extended MAPI.
Again, according to Microsoft exended MAPI can be difficult to learn.
For Delphi you can use Easier Extended MAPI, like it is described here, but that was also too difficult to learn, too much time I will need, so I found RapWare Easy MAPI components, which completely satisfy me.I don't think that I need to write too much about them, since they have very good examples about everything.