The anime does follow it to a certain point. I would say until main protagonist fist man(Kazuma) meets the child molester(Ryuho) it's relatively the same but after this it diverges so much with multiple storylines not in the anime/manga it's pretty insane. If you haven't guessed I watched the anime first and just finished the manga. ~SPOILERS~ Fister fights the main baddos alter like the anime but it happens differently and he sure as shit doesn't lose and arm loose and eye and gets frozen in ice with a dino. There sure as shit doesn't have an ALIEN INVASION[WTF!!!]. The anime however goes into depth of pedoboys reason for his angst and what that pedant is(it appears in two pages at the end). There seems to be a heavier friendship in the anime vs the manga as the friendship is heard rather than written.