[WARNING: The following review of "The Disappearance of Nagato Yuki-chan" contains spoilers of "The Disappearance of Haruhi Suzumiya," the novel / film that is the basis of this romantic comedy manga.]
If you want to enjoy the comic "The Disappearance of Nagato Yuki-chan," perhaps you should know a few things about the "Haruhi Suzumiya" light novel series, especially its fourth installment "The Disappearance of Haruhi Suzumiya," or its animated adaptation. Those who have read (or seen) "The Disappearance of Haruhi Suzumiya" may remember the storyline, in which Kyon, hero and narrator of the series, discovers one morning that with the "disappearance" of his classmate Haruhi, the world as he knew has completely changed. Koizumi's special "ESP" abilities are gone. Mikuru is as lovely as ever, but she is no longer a "time traveler." Haruhi is still delightfully eccentric, but seems to have lost the powers that could destroy the universe. Nagato is not an "alien," but an ordinary girl, much more emotional than the "original" one. Also, the new Nagato seems romantically attracted to Kyon.
Now, what if Kyon does join her literature club and accept the changed world as it is? Why not? The alternate Nagato is as attractive as the original. Maybe even better! The story of Puyo's new comic "The Disappearance of Nagato Yuki-chan" centers on this possibility, namely the romance between Nagato and Kyon, two ordinary high school students. Being timid and lacking self-confidence, Yuki Nagato tries to tell she likes him, but always falters before Kyon, who is not aware of her true feelings.
In short, this is a romantic comedy featuring Nagato Yuki and the beloved characters of Harihu series, set in the world you have glimpsed in "The Disappearance of Haruhi Suzumiya." This means there is no SOS Brigade in this comic's universe. Characters from the original series may appear, but not in the same way. Haruhi, the original's heroine, is a student of Kouyouen High School, not North High. Her role in "Yuki-chan" is naturally much smaller than in the original Haruhi series, and so is that of Koizumi, who only briefly appears in the bonus 4-koma section. Mori-san (mysterious agent of Koizumi's organization) is the school's physical education instructor, the only person who can stop the always overenthusiastic Tsuruya-san.
Instead of Haruhi, Ryoko Asakura plays a major role in this spin-off series as Yuki's best friend. She knows Yuki's secret feelings, and encourages her to confess it by setting up a Christmas party. She is not a knife-wielding deadly assassin, but a truly thoughtful person, someone who looks like Yuki's reliable elder sister (or mother).
So you might ask; can we enjoy reading it as a stand-alone comic? It depends. Yuki Nagato is cute and likable, and jokes are funny, but most references to the Haruhi franchise will be lost on the uninitiated. But remember, basically this is more a romance than a comedy. Puyo's artwork is sometimes uneven (Tsuruya-san's illustration is disappointing), but largely good. The best part is the cute illustrations of Yuki Nagato, which captures her nice personality. You will like her and follow her story.
Illustrated by Puyo (known for "The Melancholy of Suzumiya Haruhi-chan," another spin-off comic), "Nagato Yuki-chan" has been serialized in monthly magazine "Young Ace" published by Kadokawa Shoten since 2009. At the time of writing this, four tankoubon volumes have been published. I hope you enjoy reading it.