The subtitle of the book is Firms, Contracts, and Trade Structure. Here is one interesting bit of many:
…in that same year  the share of intrafirm trade reached a record 89.6 percent for U.S. imports from Western Sahara. Leaving aside communist dictatorships and disputed territories, and focusing on the 50 largest exporters to the U.S., Figure 1.3 illustrates that the share of intrafirm trade still varies significantly across countries, ranging from a mere 2.4 percent for Bangladesh to an astonishing 88.5 percent for Ireland.
In that paragraph you can think of “intrafirm trade” as basically standing in for multinationals. One motivation for this book is that a lot of earlier theories focus on international trade across firms and governments, when in fact much of what goes in is intra-firm and thus requires some more subtle theories. Chapter two of the book is an excellent introduction to how international trade theory has shifted from an emphasis on countries or sectors to individual business firms, a significant advance. A Nobel Prize for Marc Melitz and Antràs is by no means out of the question someday.