Well, there's the basic DOS from IBM for the IBM PC, MS-DOS (1.0 through 7.0) from Microsoft and DR-DOS from Digital Research. And there was the very successful DOS/360 for the IBM mainframe back in 1964 already. Which one of those do you mean?
And may I remark that I wouldn't recommend a study of the internals of any of those DOS-es to a newbie (that's the forum you posted in). Better start with using Windows 7 or Mac OS X.
And, by the way, these forums don't help you with your homework for IT 101 or so. Just study the course material.
What are the 4 logical parts of DOS?
Is it internal/external & utility commands?