Hi! Omitting where would render the sentence ungrammatical; so if you have to delete the 'where' let it be: The library we met at, is the largest in the city , or Let it remain : The library where we met is the largest in the city. Either where (adverb of place) or at (preposition) would be needed to show the relationship between met and library in the following two sentences: 1. The library 'where' we met is the largest in the city 2. The library we met at, is the largest in the city. Other examples of relationship between met and library may include: We met outside the library. We met behind the library, etc Which means a word showing the kind of relationship between the two words is needed. Thanks Syed.

Syed Wajahat Gilani has given a comprehensive answer to the question. If you omit where, then you do not have an identifier for the preceding noun! Relative clauses are clauses starting with the relative pronouns who*, that, which, whose, where, when. They are most often used to define or identify the noun that precedes them.