4. A favorite myth or myths of this deity.
5. Members of the family – genealogical connections
There aren't many surviving myths about Hestia. I have briefly mentioned two of them on previous days, so the only myth really left to explore is that of her birth. Since that also gets into her family connections, I'm including that as well.
Before the birth of the Olympian Gods, the generation of which Hestia is a part of, there were the Titans. There were twelve Titans in the first generation, and Kronos ruled them. Kronos was told that he would eventually be overthrown by one of his own children (in most versions of this myth, Kronos overthrew his own father, Uranus, to gain his power). To make sure his rule wouldn't come to an end, he swallowed each of his children as his wife, Rhea, gave birth to them.
Hestia was the first born, and so the first to be swallowed by Kronos. Rhea also gave birth to Demeter, Hera, Hades, and Poseidon, and they met the same fate as Hestia. However, when Rhea gave birth to Zeus she hid him away, and tricked Kronos into eating a stone instead. Zeus grew up, and forced Kronos to throw up his siblings, who came out in reverse order they were swallowed. This is why Hestia is both the oldest and youngest, and why she is sometimes called "first and last," and why she was frequently given the first and last offerings at banquets and some other events.
As mentioned in an earlier post, Hestia was a virgin Goddess who never married, and did not have children of her own, although her siblings had quite a few children, and so she is related to quite a few other gods in that way.