When writing the title of a book, one is supposed to capitalize a preposition if it’s the first word in the title, but to use lower-case if it’s not. For instance:
A Tale of Two Cities
But if a preposition is the last word of the title, it looks strange not to capitalize it, too.
Mr. Britling Sees It through.
Should the preposition in such a case be capitalized?
The first and last words are always capitalized. Some prepositions are capitalized and some are not, depending on the house style (i.e., the particular publisher). Longer prepositions are capitalized, but there are differences of opinions about what constitutes “long.” Most places use a list.
Close. It’s not a preposition, but it’s not an adverb, either. It’s a particle. That is, it’s part of the phrasal verb “to see through,” which means “to complete a project” (or “to understand the motives” as in “I saw through him.”)
This isn’t really a grammar question, but a style question. I would just consult a style guide for the answer. The part of speech isn’t that important in this situation.