Aptly named, this film.
Mad - Yep, we got crazy. Max is kinda nuts, with random people from his past popping into his head regularly. It's heavily implied that he's seeing members of his family that he failed to save, and he's been less than sane since. (Possibly someone who had seen the previous three Mad Max films would recognize some things in those flashbacks, but I haven't watched them.) And the world at large is pretty crazy, being a post-apocalyptic wasteland.
Max - Protagonist named Max, check. Tom Hardy does a fine job in my opinion - not an amazing performance, but that's all right since the character doesn't really do much outside of a whole lot of stunts. Max isn't your usual hero material, what with the insanity and all. The evolution of his relationship with the other lead character, Charlize Theron's Furiosa, doesn't feel all that crazy, though. Max goes from captive to mutually suspicious no-choice-but-to-work-together travel companion to trusted fellow warrior/leader/perhaps love interest. No surprises there.
Fury - Just about everyone's angry about something. Furiosa and her escaping girls are mad about mistreatment (with cause, I'm sure). Max is angry that he was taken captive and lost his car. The bad guys are pissed about the escapees, some other bad guys are mad that their underhanded deal got wrecked, and so on. Plenty of fury to go around.
Road - So many post-apocalyptic wasteland vehicles to blow up, so little time! There are a whole lot of high-speed chase and battle scenes, mostly with all kinds of explosions and fire. The action is well executed in my opinion. I like exploding vehicles as much as the next guy, and these kept me entertained the whole way.
Mad Max: Fury Road delivers exactly what it promises - lots of action in a post-apocalyptic dystopia. The plot and characters are there mostly to support the action, and do that well. You can read some deeper themes into the story - mistreatment of women, dangers of a cult-like society, you can't go home again - but I prefer to take it at face value as a fast, fun ride.