Also curious because the Italian authors failed to notice the very significant cultural differences in this essential social gesture. It should be obvious just by the terms themselves. In English we use "shake hands" and "handshake." The Italians use darsi la mano or stringere la mano for the verb- literally, to give (one's) hand or to squeeze hands. The noun is stretta di mano. Now in my experience this is what Italians actually do. I, as an American, would shake hands as advised by the Brits (which is apparently where we got it from.) Grasp hand, shake firmly but not too vigorously about three times. What ended up happening in Italy was that Italians (especially women) would give me their passive, unmoving hand, and I would agitate it up and down, with mild comic effect. Perhaps the Italians themselves didn't think it was just mildly comic.
I won't even go into the timing and use of handshaking, or hand squeezing if you will. The British newspaper says that there is no difference in men's and women's handshakes. I disagree- there is vast interpersonal difference in handshake styles, including gender differences. And Italians, especially women, relatives and close friends, will often do the kiss-on-both-cheeks thing as a greeting, which I never took to.