This new manga is topping the sales charts in Japan and I think for a good reason.

I just started reading it (I am just into the second chapter) and I am already hooked.
First let me spend a few words on the drawings. The backgrounds are quite nice and polished, but the characters, although nice, could be less "noisy".
I think this kind of style is instead very appropriate with the giants (or titans). They are strange, distorted human forms with the skin of their faces revealing all their theeth in a wicked grin. Their body proportions are usually off enough to give them an even more monstrous appearence.
The faces of the characters are nevertheless pretty good at conveing emotions.

The characters' fear in the face of an impossibly stronger predator is well represented. Imagine if you were face to face with a monstrous 15 meters tall man with a wicked grin and the will to eat you...

This plays on our instinctive fears of predators. It's true that today humans are at the top of the food chain, but it hasn't always been like that.
Probably if lions would evolve an intelligence they wouldn't know this kind of fear as they have no natural predators (normally), but for us the fear of being preys, of being helpless in front of a strong predator is something we can understand well.

I don't remember another manga with such a strong emphasis on this aspect and this certainly is a good thing!

The only small complaint could be that the drawings quality is not always the best, but seeing how the series has just started I think the author has plenty of time to improve.

I definitely recommend this series!