The Elements of Typographic Style is a book written by Canadian Robert Bringhurst that is widely considered the definitive guide to typography and design. The book covers a wide range of topics related to typography, including the history of type, the anatomy of letters, the principles of design, and the use of type in different contexts.
The title lettering of the book Elements of Typographic style is most likely set in Arno by Robert Slimbach. “The Elements” part in Arno Display and “of Typographic Style” in Arno Display Italic (the letter “y” and “l” in swash alternates). For the author's name, it is similar to Poetica typeface by Robert Slimbach.