“Today, on this island, a miracle happened: summer came ahead of time.”
This is the opening line of the novel. The idea of summer coming "ahead of time" reflects the oddity of the situation. This line indicates the beginning of the seven-day apparition, in which the island is filled with the replications of its former inhabitants. Unsurprisingly, the narrator has no idea what's going on, and he spends the majority of the book understanding and coming to terms with the nature of these suddenly existent island-mates. The reference to the happenstance as a "miracle" is also predictive of the narrator's view of the instantaneous appearance and disappearance of the people; for the first half of the book, this occurrence seems to be supernatural.
"I have given you a pleasant eternity!"
In this quote, Morel's philosophy and purpose for creating the experiment come to light. He has a desire to live forever, as well as genuine goodwill for his friends. His experiments with his invention have led to his belief that if people are captured by recordings for a set amount of time, and those recordings are processed through his machine and projected into reality, then the soul can be transferred to this indestructible copy, thus preserving it for eternity.
At this point in his speech, Morel is announcing his gift to his friends: he has been recording them having fun and relaxing all week so that they may have a "pleasant eternity," living out these seven days over and over forever.
“The real advantage of my situation is that now death becomes the condition and the pawn for my eternal contemplation of Faustine.”
This quote, taken from the last pages of the novel, reveals the narrator's dying plan to immortalize himself for the purpose of enjoying Faustine (the woman from Morel's recording with whom he develops an obsession). He lives the week over and over, devising actions and lines for him to enact that make it seem like he's interacting lovingly with Faustine, and then he records himself doing so. In this way, he inserts himself into Morel's recording and ensures that he will always be present when Faustine is present, integrating himself into her eternity.
Death is no longer an obstacle for the narrator's contemplation of Faustine; on the contrary, it is its necessary condition. Before death, he must worry about sustenance and discovery, but in death, he manipulates its conditions to spend eternity in carefree enjoyment of his Faustine.