Despite its curious title ("zetsubou" means "despair") and the ultra-pessimistic protagonist who keeps thinking about dying, "Sayonara, Zetsubou-Sensei" is a comedy. Yes, it is a comedy and not a usual one. My advice is, 1) Don't take anything in the comic too seriously; and 2) if you don't get some of its jokes, just skip them and read on. I am Japanese and after repeated reads I still don't get some of the comic's gags.
"Sayonara, Zetsubou-Sensei" revolves around one young, eccentric teacher Nozomu Itoshiki. Always depressed and thinking of dying (that's what he says, anyway, and he has a guidebook for that purpose), Mr. Itoshiki is actually a good teacher, well, a much better teacher than you might imagine, for these unique (mostly girl) students in his class including Miss Kahuka (her penname), the most optimistic girl in the world, and the stalker student, a "shut-in" student, and a very shy student who keeps sending poisonous email, and....
The comic started in 2005 and has been serialized in "Weekly Shonen Magazine" since then. The unpredictable comedy is based on the characters' exaggeratedly eccentric behaviors, which often lead to unexpected and hilarious results, but the comedy also heavily relies on the parodies and pop culture references. As more than four years have elapsed since the first publication of the series, some of the gags are now obscure, hard to understand even for Japanese readers. Fortunately there are many jokes and the character-driven story never lets up ... and all the girls are charming and funny ... in their own peculiar ways.
Manga artist Koji Kumeta has created a very unique world in which old-fashioned Japanese culture such as kimono costumes and old wood school buildings co-exist with modern technologies like cell phones and pop culture references. His illustrations are meticulously drawn and not a single space is neglected. Sometimes jokes are crammed into such small spaces as TV screen or newspapers the character is casually watching.
[TRANSLATION] This means that translation is virtually impossible. I was truly surprised at the decision of Del Ray to publish the English edition because their job must have been extremely a tough one. Though I disagree with some of the words they chose (I think it is "National Team of Japan" not "Representative"), English translation is very good as a whole. Del Ray's book has also a 12-page translation notes explaining some of the obscure references to Japanese culture.
[NAMES] Most characters have strange names. I never met someone with a name like "Itoshiki," which is part of the comic's jokes. The fact is most character names are puns which are often very silly read in original Japanese. For example: the timid girl's name Meru Otonashi means "Silent Mail"; Chiri Kitsu means "Exactly"; Kaere Kimura means "Go Home, Kimura" and is also a joke on Japanese pop singer's name Kaera Kimura; Abiru Kobushi means "Get Hit with a Knuckle"; Kiri Komori means "Always Confined"; Tsunetsuki Matoi means "Eternally Stalking"; "Nami Hitou" means "Ordinary" and so on.
Volume 17 of the comic has already been released in Japan (May, 2009), proof of the popularity of the comic. I sincerely hope that Del Ray will keep publishing the book, but you may not find "Zetsubou Sensei" as funny as I do for the reasons I explained above. I believe it is worth a try, though, for the delightfully strange characters you will meet in the book.