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I had a similar question about the curriculum. I suggest looking at http://web.mit.edu/catalog/degre.engin.ch6.html and look at the classes for Course 6-3, which seems to be the undergraduate Computer Science program.
I can't give you the generalized answer, but 6.001 is not the next step after 6.00. 6.001 is an older lecture (>10 years old) that is based on the language LISP. It is an alternative to 6.00 but I wouldn't recommend it as no one else is studying it and you won't have a group to learn with.
ejerud's right. I was just about to learn 6.001, and there comes 6.00.6.00's videos are not that clear