The appropriate preposition here is "on." The phrase "the book is on the shelf" indicates that the book is resting atop the shelf's surface. Using "in" would suggest that it is contained within the shelf, while "at" indicates a general location without specificity, and "under" implies being below something. Mastery of prepositions that describe location is crucial for clear communication in English. Misusing them can lead to misunderstandings about where items are placed; for instance, saying "the book is in the shelf" distorts the intended meaning. Clarity in language is essential to ensure that listeners understand the details about locations and actions accurately.
Preposition 
Preposition