As implied by the question itself, the standard term for the behaviour itself is one-upmanship.
Although alphadictionary.com is prepared to accept one-upman as a word in itself, to be honest I think they're in the minority on that one. In the absence of a convenient single-word derivation from the standard term, people usually just say it using more words - for example...
He always has to one-up everything you say. (lots of written instances in that link)
Most of us indulge in one-upmanship from time to time - it's part of normal social interaction. It only becomes tiresome with those few people who do it excessively. The most common single-word adjective I can think of for such a person is competitive. Which has lots of other shades of meaning, but when used in the context of how someone interacts socially, I think most people will know exactly what you mean.
user653's comment to @Barrie's answer reminds me of my favourite example from Dilbert...
When speaking about a textbook used in class, it's a fairly common occurrence that teachers are unable to complete the book by the end of the scholastic year (or semester) especially if they have used supplementary material or the same textbook has to be studied the following year.
To dip into a book suggests that the book itself might not be very interesting or useful, if it were we would spend a greater time reading or studying from it. That expression is more commonly used in conjunction with epic novels or hefty volumes, think of an encyclopedia. How many people actually read an entire book set from beginning to end?
Furthermore, a dip, if you consider one of its meanings is a quick "dive" into liquid to then reemerge. Ergo we dip biscuits into teas, we dip our toes in the water to test its temperature, and we dip our food into sauces or creamy mixtures.
The addendum says that the class covered only several chapters, the expression used by the OP is perfectly suitable, and one that is universally recognized. In fact Google books records 76 results for "we covered chapters".
I would suggest that a sentence similar to the one below, explains the situation adequately.
In this course we covered chapters 5-10, and plan to complete the book by next semester/term/year.
If we substitute the verb covered with dip, the meaning changes quite dramatically.
In this course we dipped into [textbook name], and plan to complete it by next semester/term/year.
The above sentence seems to imply that the class studied extracts in a haphazard, casual and superficial way. The Free Dictionary defines dip as: To read here and there at random; browse Contrast it with the verb, cover, which means all of the following: to deal with; treat; examine; investigate; refer to and you'll see why I have my reservations. Likewise the same is true for: browse; skim; scan; flick though, and leaf through all of which suggest a smattering of knowledge, where nothing is read nor understood in any detail.
Finally, the OP's request for a single word which expresses the concept of studying a few chapters in a book to return to it sometime in the future is unrealistic. Such a complex concept needs explanation. But we do have the phrasal verb put aside (also set aside) which means turn away from and put aside, perhaps temporarily, and place to one side.
Best Answer
You might refer to Rayman as ethereally-limbed or invisibly-limbed; or perhaps call him disjointed, a word that means “(figuratively) Not connected, coherent, or continuous”. (It appears that Rayman is missing all his arm and leg joints, as well as his neck.)