In Fahrenheit 451, briefly explain the significance of each of the three section's titles:"The Hearth and the Salamander," "The Sieve and the Sand," and "Burning Bright."
"The Hearth and the Salamander" refers to Montag's job (the salamander) and his home (hearth--which interestingly enough, historically, was the center of the home at the fire). Referring to his fireman's uniform:
...she seemed hypnotized by the salamander on this arm and the phoenix disc on his chest....
The significance is that his job enables him to live, afford a home and all that comes with it. However, whereas culturally the hearth symbolizes the heart of the home and the comfort of family, Montag does not have this. As time goes on, he is less connected not only to the job, but also from his wife.
"The Sieve and the Sand" refers to Montag's inability to absorb the meaning of the words in the books he is trying to rapidly read before having to return them; in one specific case, he is reading the Bible. He is reminded of a childhood memory of trying to fill a sieve with sand, an impossible task—which is what it is like for him to rush through reading the words when he cannot make sense of them or recall what he has read.
Figuratively, "Burning Bright" refers to Montag's passion to read and learn once he throws off the shackles of society's control with regard to reading, and free thought and expression. Literally, it can refer to society at the end when the bombing begins and the buildings are burning, ending the way the culture has been controlled up until the end of the book.