Elegiac, Precocious, Shadowy
It shouldn't surprise you to know that, in a book like this—with such a complex, intertwining plot—the writing style is also varied and complex. Throughout this twisted History, Krauss likes to alternate chapters that are, as we'll term them: elegiac, precocious, and shadowy.
Let's start with the first type of chapter and our vocab word of the day: elegiac. Since his heart attack, Leo is both waiting for Death's inevitable embrace and adamant about squeezing out every last moment he's got left. His willingness to set his story to paper is Leo's way of balancing these competing aspects of himself—both honoring his life and preparing his legacy.
Now, for precocious: Alma's chapters are stylistically energetic and unpredictable, leaping back and forth between ideas and temperaments. Her numbered headings serve as everything from stage direction—"20. Awake in the Dark" (8.62)—to declaring minor epiphanies—"21. She Must Have Gotten Married!" (8.63).
And finally, we also have a shadowy style to contend with. Yes, Litvinoff is one shadowy fellow—not shady, as in sketchy or untrustworthy (read more on that in Zvi's character analysis), but we never really get a handle on who he is, or what he's all about. It's no accident that we don't learn Litvinoff's friend's name—let alone whatever else he's up to—until very late in the story.
Oddly enough (in case you haven't noticed it already), these different styles are directly related to the different narrators we get in The History of Love. With each new voice comes a new style, so feel free to check out the "Narrator Point of View" section if you want to read up on these distinct voices in the book.