I don't think there's an exact term for this. They look a little like pull quotes (usually used to mean repeats of a quote in an article printed in large type in the margin or text column, which the main text flows around, so not exactly the right definition) or block quotes / extracts (still not exactly what you have). The term "deck" is also maybe applicable, though, like the other terms, not quite right (decks are introductory paragraphs printed in display size or special typeface). I might go with "extracts," though as I said, that has a slightly different definition of its own.

Summaries.

Thanks, Joshua Langman. Those terms help a lot, at least as tools for comparison. I think you're right that there's not quite an exact term for them, but one can certainly work with what you're offering.

Nick Shinn, not summaries. My question was a bit vague, but as JL points out, the main text "flows around" these italic bits in a way that makes them function differently than summaries or superordinate decks.

They are summaries, at least according to the introduction, which states, "For quick immersion, we suggest skimming Part I by reading the italicized sections only."

Isn't that the way summaries work—defined as “a shortened version of a text that highlights its key points”?

Alternatively, they could be considered as subheadings, in that they introduce ideas which are expounded upon in the immediately following text. Paragraph-length subheadings, that is.

However, on a purely typographic reading (disregarding content), as there is no variation in the body text, other than style, it is merely emphasis, which is generally done by going into italic or bold face, or perhaps a sans. It could be compared with a block quote, which is a similar interruption of body text. So how about "block subheading"?