why does Montag read the poem "Dover Beach" to Mildred and her friends? Does the poem signify any important themes in this novel, "Fahrenheit 451".

Montag reads the poem to not only Mildred, but also the friends she's tied herself to because he is trying to tell them that the world they are living in is like a long beautiful strap or belt thats been rolled up (hence "Lay like the folds of a bright girdle furled")and all we, as society, have to do is unroll all the beauty and possiblity that we have so tightly hidden away and nearly forogtten. The poem goes on to read "...like a land of dreams...and here we are as on a darkling plain / swept with confused alwarms of stuggle and flight / where ignorant armies clash by night."(p.100)Meaning here we are, in a place of such awesome potential and we're so ignorant to it that we throw it all away and deliberatly demote literature and the ability to think, to question, to try and understand. We are burning away all possiblities for sincere happiness.(speaking, of course, of Montag's society)
Montag also chooses to recite a poem to Mildred and her friends because he knows it will disgust them. It shows he is unafraid of their opinions of him and that he's up his mind to save the very thing they are agreeing to destroy by simply living their ignorant lives.
Hence, this is why Ms. Phelps is crying by the end of the poem, Montag has touched her in such a way that she "just doesnt know...just doesnt know".