Who is writing letters to whom? What is Walton's present occupation?

As the novel opens, Robert Walton is writing letters to his sister, Margaret Saville. These letters provide the frame for the central narrative, introducing the reader to Dr. Victor Frankenstein after the inciting events of the story have taken place, such as Victor's creation of the creature. The letters raise our curiosity, yet they convey a sense of uncertainty: they may, in the end, be the only documentation of Walton's arctic voyage:

if I succeed, many, many months, perhaps years, will pass before you and I may meet. If I fail, you will see me again soon, or never.

Other letter-writers include Alphonse Frankenstein, Victor's father, who writes, among other things, to tell Victor of William's murder, and Elizabeth, Victor's foster sister and bride, another person the creature kills.
Walton is presently an explorer who is taking risks in the hopes of making important discoveries in the arctic. Victor tries to warn Walton not to make his mistake and become too ambitious.

Frankenstein begins with a series of letters written by a man called Robert Walton to his sister, Margaret Saville. Walton is an English sailor, the captain of a ship that's currently exploring the icy wastes of the frozen north. Like the man that he will soon meet and who will change his life completely, Walton is a scientist, an explorer, and someone who wants to push beyond the boundaries of human knowledge.
In his letters to his sister, Walton reveals himself to be a lonely individual without any real friends. It's this sense of isolation that draws Walton to Victor Frankenstein not long after he discovers him frozen half to death on a huge sheet of ice. Walton's desire for true friendship is interesting in that it anticipates the Monster's need for a mate later on in the story. We're still at an early stage in the book, but Shelley is already establishing some of its key themes, one of which is the fine line between man and monster.