M×0(Emu Times Zero) is about a hot-tempered boy named Taiga Kuzumi who has failed the entrance exam to Seinagi Private High School. With little memory of what had actually happened, he sets out to confront the girl who had burst out laughing at him during his interview, sure that she is to blame, only to be mistaken by a teacher for trying to sneak out instead of in. Turns out that Seinagi is actually a Wizarding School, and due to a complicated chain of events ending in said teacher being blown up, now everyone believes him to be an elite magic user—when he can't use magic at all!Now Taiga has to put his wits to the test in order to keep up that cover, or both he and the teacher will be in very big trouble.
Taiga many times, but the one that stand out the most is him trying to protect the girls from the other boys using magic to peep. Surprisingly he was caught trying to help and punished by the females.
A little bit later after the student body knows him a bit better he expects to be punished for somehow ending up in the girls only swim time, but they just laugh and say it's OK because they know he didn't mean anything bad. It probably didn't hurt that he just saved around half a dozen girls from drowning, though.
Kuzumi Kokuha; every appearance has her kicking somebody's ass—usually Taiga's, and someone else's, too
Mikuni, Hiragi's friend, unlike most other girls, uses direct physical fighting methods.
All Love Is Unrequited: Mizuki likes Taiga, but he is blind to her affections. Koishikawa likes Mizuki, but she disliked him even before she started to crush on Taiga. Lucy has a thing for Taiga, but he can't even fathom loving her or Mizuki because he is crazy for Hiragi. Who also has a thing for him. And then the series ends without settling any of the romantic subplots.
Anti-Magic: Taiga eventually trades in his fake magic card for one whose sole ability is to use up the points stored on it to create an anti-magic field. After sufficient training, Taiga is able to control the field's size, shape, and location around him.
Awesomeness by Analysis: Taiga manages to defeat several powerful mages by seeing their power and using their own limitations against them. During the Class matches he defeats two people, defeated one forced the other to retreat, only taking one injury because he knew exactly how to work around their power after seeing it once before, and he only used some twigs and two rocks.
Badass Normal: Taiga's older, shorter sister Kokuha. She makes Taiga look positively weak.
Badass Boast: Taiga uses this to avoid fights, and get out of performing magic in class. It has a decent success rate.
Taiga: "What is this? Your level isn't high enough for me to use magic. Since this is nothing, how about you go away and we can do this some other time?"
Butt Monkey: Because his whole class thinks that Taiga is invincible because of his magic skill, they use him to test out new spells and anything dangerous. It prompts him to hide from them a few times.
Determinator: Taiga in general. Exemplified when he was in a spirit form he tried so hard to climb a vertical wall that he caused his real body to start bleeding. All so that he could gain a little more power, and make Hiragi's dream come true.
Deus Exit Machina: Lucy is continently absent during the Cultural festival when they were dealing with the bomb threat. Her Mandrake Network and her ability to inform the teachers in a completely anonymous way would have made things a lot easier for Taiga and team. Taiga lampshades this.
Tokita Mako's face is either always hidden, or only her mouth and chin is seen. This is part of a joke that her chest is so big that one can tell who she is with just her chest alone.
Most of the Third-Year Magic Executive Committee members faces are not shown.
Fake Ultimate Hero: Taiga. Everybody thinks he has a Gold Plate and is capable of destroying the Home Ec room with one spell and defeating a teacher. Of course, he can't use magic period and has to bullshit everything.
Gang Of Bullies: Taiga beats up one absent mindedly, beats one up to take out his frustration, and got kicked out of his first school for defeating another. Kid does not like bullies.
Gender Bender: Taiga Kuzumi after he was sprayed with a magic medicine called Lady Go.
Goal in Life: Both Hiragi and Taiga have the same goal: to obtain a gold-level plate before graduation so they can revive Hiragi's mother. Though Hiragi has no idea Taiga plans on using his wish at graduation for this in the event she fails.
Inspector Javert: Vice-Principal Kagami despises any rule-breaker regardless of mitigating reasons. He starts an investigation of Taiga due to inconsistencies that could expose not just Taiga's unorthodox and rules-violating entry into school but also ruin Hiragi-sensei and the Principal.
Loophole Abuse: In the lotus eater machine test mentioned below after Taiga and the other two that passed pull Ise Kaoru and Hiragi out of theirs stating that there is no rule that says they cannot.
Lotus-Eater Machine: Part of the magic exams requires you to leave a Lotus-Eater Machine room within 10 minutes. If you do, you pass that portion but lose your memories of inside the room. If you don't, you keep your memories but fail.
Lovable Coward: Taiga in many aspects, he does everything he can to get out of an actual fight so that he can stay in one piece and keep his reputation. He can and will fight when he has too, but bluffing, running, and letting his classmates fight for him are his favorite tactics. This only applies to magic fights, any other threat he is the first person running in the most dangerous direction.
Love Potion: Proving that he was under the influence of one is how Taiga and Mizuki become acquainted.
Made of Iron: Taiga goes though the meat grinder pretty much every magical competition because he is sent though the most dangerous and difficult parts, and he has no magic, but he always manages to keep right on going no matter how damaged he gets.
Rendou Niigaki who retired from teaching at the school but helps Taiga level up his M0.
Otoya Hanasaki, the previous principal, Otome's father, and the only one who can create Black Plates.
One-Liner: Hilariously parodied with Taiga, who's forced to come up with increasingly sappy repartees to cover up for his lack of magical talent. Of course, the excuses never fail to impress his audience.
Our Ghosts Are Different: Otoya Hanasaki possesses Taiga's body while the later is working on an upgrade of his plate. While Taiga cannot use magic, the ghost possessing him still has access to his magic he had in life. Hilarity Ensues
Parental Abandonment: The only person we ever see in Taiga's family is his abusive older sister Kokuha. Do they never question why he come home beaten up from school just about every day?
While the family is put far in the background, we do know they exist. When Taiga is sent back in time to fix his entrance interview his mother asks his sister to bring his entrance folder to him.
In the Principal's office, we have seen Principal Hanasaki playing against Hiragi-sensei. Hiragi-sensie almost always won.
In the Cultural Festival Arc, bombs have been planted around the campus and the bomber says the Magic Executive Committee must win against his people to get hints to where the bombs are located. One of the challenges is playing shogi. Hiragi, as she is Kuzumi's assistant, plays this challenge. She not only beats Daimon but thinks he' the bomber's ally, he doesn't even realize her next opponent is the one she has to look for and so plays him without any hesitation.
Spider-Sense: Taiga has a simple version of this because of living with his sister Kokuha.
Warrior Therapist: Taiga pulls this in his fight with Ise and in the process saved his friendship with Nagai. Taiga was happy to get out of that fight with as few injuries as he did, and surprised it worked.
Weaksauce Weakness: Hiragi can turn herself invisible with her powers, but when Taiga had to face her once he kept yelling bad puns to make her laugh and give away her position.
Heart Is an Awesome Power/Shut Up, Hannibal!: When Kuzumi defeats Daimon, despite the latter's powerful offensive magic, Kuzumi points out when Daimon faced against Higari-looking-like-Kuzumi, she marked his King's crown with the last of her magic and that is what allowed Kuzumi to track him even in the dense forest.
What Measure Is a Non-Human?: Students and teachers alike see no problem with grinding up fully sentient Mandrakes, after all even if they are mentally the same as humans and feel love and pain just as we do they are just ugly plants if you take away their illusion magic.