Assassination Classroom is one of the rare stories where the anime adaptation follows the manga very closely. We all know that anime adaptations generally follow the storyline of the manga version, or in uncommon cases, the light novel versions. Anime adaptations usually consists of certain tweaks or changes to the storyline from the manga or light novel.
One example would be Card Captor Sakura. In the manga, there are only 19 Clow Cards in the story, whereas the anime adaptation included an additional 34 cards. Another example would be Black Butler (aka Kuroshitsuji) where the second season anime adaptation is purely created for the anime adaptation only and it does not exist in the manga version.
Changes made to the story for the anime adaptation may not necessarily be a bad thing albeit it is generally viewed negatively by fans. However, this is not to say that anime adaptations changes the entire storyline (probably with a few exceptional cases like Black Butler) from the manga. I would say that the vast majority of the anime adpatations follow the manga storyline and plot as closely as possible, but they tend to add in a few other things in hopes to "spice things up" (like Card Captor Sakura).
The great news about Assassination Classroom is that there is practically little to no difference between the manga and anime. Hence, watching the anime is almost as good as reading the manga version.
(Picture Source: Anime Bird thru' Google Image Search)While the series is already a rare breed in the anime adaptation world where it follows the manga storyline very closely, it is also one of the rare stories where two major story plots are happening at the same time.
The first, as the synopsis of the story in this site says, is that the students' mission is to kill their homeroom teacher before graduation. If left unchecked, their teacher may blow up the earth and destroy humanity in the process.
(Picture Source: SpaceBattles thru' Goolge Image Search)The other major story plot that is not known unless you watch the anime is destroying Asano's, the school principal, educational philosophy.
(Picture Source: LuRa's Anime Blog - WordPress.com thru' Google Image Search)Not giving any spoilers, I would say that Asano's philosopy technically isn't wrong, it's just the way he applies it. Ironically, the one person who agrees and shares the same philosophy as him decided to use it differently, hence, a different kind of result. It is also the reason I said that the philosophy isn't exactly wrong.
Anyway, the story itself is fun to watch with lots of comedy that fits the narrative. While the comedy and the action scenes were intriguing, my personal favourites are the school exams scenes. Those are really the best that whenever I try rewatching the series, I always look forward to them.
(Picture Source: leatherbound-青月 - WordPress.com thru' Google Image Search)