Is this sentence grammatically correct? This is from a book. Which is the subject and the verb? I thought "This" was the subject here.

This, despite the fact that a number of recent studies suggest that any deep sleep - whether in an eight-hour block or a 30-minute nap - primes our brains to function at a higher level, letting us come up with better ideas, find solutions to puzzles more quickly, identify patterns faster and recall information more accurately.

See a translation

EDIT: After rereading the article with a fresh mind, I've realized what's going on. This is valid English, but quite colloquial and probably not a sentence you ought to analyze using conventional subject–verb considerations.

"This" refers to everything the author has said before (i.e., how people are trapped by the belief that they need to get a perfect 8 hours of sleep, and how the stress arising from that belief is actually making them less able to sleep, fueling a vicious cycle). In terms of meaning, it can be replaced by "This situation exists" (i.e. "This situation exists, despite the fact that...") or "This is the situation" (i.e., "This is the situation, despite the fact that..."). However, just saying "This" is more impactful and conveys more outrage regarding the situation (think of it as the writer shoving the situation in the reader's face and saying "THIS").