Who is Robert Walton writing to in the first letter in Frankenstein?
Robert Walton is writing to his sister, Mrs. Margaret Saville, in England. He has been away at sea for six years and by his descriptions in his letter, he is an ambitious man who might be gone a great deal longer.
The purpose of this letter, and the others that follow, are to frame the story of Victor Frankenstein within the story of Robert Walton. We come to know Walton via his letter to his sister, and it turns out that he and Frankenstein have much in common.
In this first letter we see that Walton is about to undertake the most significant and most dangerous part of his journey. This part of his tale then mirrors the journey of Frankenstein quite closely. In this letter we see an ambitious and focused man ready to take on anything to accomplish his dream. Shortly, however, he will run into Frankenstein, who will be, in many ways, what Walton himself might be in the future if he does not change his ways.
Walton is writing to his sister. He is writing to her largely for the reader's benefit so we know who he is and why he doing what he is doing. His sister is unnamed, but she is to serve as the reader surrogate. The sister does not really come back into the story until the very end, wherein we see how the story ends and the characters react to everything.
And as an aside, the photo in the summary is incorrect. The Universal Frankenstein film with Karloff as the monster was released in 1931, not 1935. The picture itself looks more like a scene from the 1935 sequel, Bride of Frankenstein.