Itsuki Iba is the son of the founder of Astral, a company hiring out magicians to those who need their help, and took over as president after his father disappeared. The problem is that he's weak-willed and weak in magic... except for the Glam Sight in his right eye, which turns Itsuki into a capable commander, but at its own price.Based on a light novel by Makoto Sanda, adapted into an anime by Zexcs.
This anime contains examples of:
The Ace - Deconstruction. Older mages rarely interact with the cast, and almost never appear for long. The exclusion is Association's investigator Kagezaki, who is apparently powerful and knows a lot, but just stands nearby with a confident smile and interferes as little as he can, even in dire cases. He's also a royal pain in Astral's collective butt as their curator and while he never pushes them too far, seems to enjoy using Jerk Ass Facade and constantly keeping them on their guard.
Big Damn Heroes - Adilicia is fond of pulling these off, most notably in episode 20.
Bilingual Bonus - In the Whole Episode Flashback of Adilicia's and Honami's past, there's a gravestone with clearly legible text written on it in English. Problem is, the text is written with Norse runes. If you can read them, you'll find a few rows of Bible verses, Psalms 22:15-16 and 81:1-4, more specifically.
Blade Run - Sekiren lands on Daphne's foot and tells her to calm down when she tries to kick him.
Blessed with Suck: Itsuki's Evil Eye is very useful, to the point of winning almost any battle he uses it in. It also gives him a lot of pain when there's a lot of magical energy nearby, and it can make him insane.
The Chains of Commanding: Itsuki knows he's way over his head and is pretty much constantly in panic on the early stage of his "career". In manga, he repeatedly tried to refuse becoming "the president", but the rest of Astral team do their best to trick, plead and guilt him into accepting it, and then into staying.
Gone Horribly Wrong - Attempts to apply magical power for either taking a more direct control over magic, or resurrection, or achieving immortality turns mages into bubbling Nightmare Fuel. There was no doubt left why exactly such things are taboo.
Grade School CEO - Itsuki and Adilisia aren't babies but still are too young when they were put in charge. Justified, as in anime, the Association had to either gamble with 'heirs by blood' or with more experienced possible heirs being too irresponsible or unavailable. They had a reason to suspect a taboo violation in Goetia, but no idea which survivors were involved, then Daphne declined the office, further limiting the possibilities. Astral could be led by Judaicus Tholoide, who can just leave Astral on their own for years, then hire them, then suddenly attack — not personally, but through a little girl — then claim it's his heirloom. With such alternatives, even a magically inept youngster suddenly becomes the more sane choice.
In manga, when Itsuki tries to squirm out of the position, Nekoyashiki quotes a rule: "Priority for the founder's leadership must be given to blood relatives", and then avoids getting into details.
Orphan's Ordeal - Itsuki has to deal with the whole business because his father disappeared. Adilisia is more capable in her role, but she also must hide the circumstances of her father's demise as shameful for her family and Goetia.
Our Ghosts Are Different - Kuroha quietly walks all the way from a lost soul haunting the hospital to rather powerful guardian spirit. A bunch of ghost children just can't accept their accidental death and are released once they got the celebration they wanted.
Shown Their Work - The light novel/anime really goes the extra mile with their knowledge of the occult, for example Kuroha's Tree of Sephirot not having the branches for Memory or Past. When the anime first aired one Fansub would add notes at the end of each episode detailing the occult usages throughout, from the histories of Addie's Demon Summons right down to translating and explaining the sutras that Mikan and Nekoyashiki chanted.
Spoiler Opening - The opening shows Sekiren and Fin, who don't appear until episodes 16 and 22, respectively. Furthermore, they show Fin in a clearly antagonistic way, even though he's introduced in the show as a seemingly good guy.
Undying Loyalty - Daphne. She's older half-sister of Adelicia and had the same blonde hair and green eyes; since the similarity was too obvious, she had to sacrifice her colouring so not everyone asks obvious questions. She protect Addie as much as she can and refused to take over Goetia as a more experienced mage. No wonder the guy who is romantically interested in her is the rugged bushi-style warrior Sekiren.
Un Equal Rites: A dazzling array. It seems that magical traditions used by more than two people who get on screen at all are a minority — and the series has lots of magic users. Though the existence of a Wizarding School illustrates that there are must-have basics.
Religion is Magic - Namely applies to Mikan's Shinto magic, which is based on actual Shinto rites and chants. Honami also applies somewhat through her chants calling on Celtic deities.
Ritual Magic - Names and forces are invoked all the time, but usually most powerful and complex magical operations are done the long way. Though such procedures don't make personal power of the caster(s) and external boost by artefacts and ley lines any less important.
Summon Magic - There's some evidence that Solomon's school of magic is more than this, but commanding demons is a signature and status thing, so Addie is a dedicated summoner to the exclusion of everything else and tries the same solution for every problem: "summon demon, summon demon, summon demon... summon angel... summon demon".
What Measure Is a Non-Human? - Itsuki has a demonstratively very lax idea of what is 'human' — even for mages — and consistently applies it, be it Cute Ghost Girl or Monster of the Week... and doesn't see even a dragon as something too different. He's charming enough to make it work more often than not, though it isn't terribly helpful when the creature is remotely controlled or inherently inimical.
Widow Witch - Technically, Diana is not a widow, but she wears a widow's outfit (after giving one too powerful artifact to one too wrong guy) and is a head of magical supplying company Trismegistus. Neither precludes her from having a sense of humor.