At his death, the great sage used the new magic he developed to reincarnate into the future. However, he was deemed to be talentless and abandoned in the forest of monsters where he was picked up and raised by goblins. To repay them, he helped them evolve and taught them magic. The story of the abandoned child who will build what would be known as the great empire of monsters.

From author's site:
I love math. Just after the high school entrance ceremony I meet a beautiful girl, Milka. Milka is a mathematical genius. She gives me many math problems and shows me many elegant solutions. Milka and I spend a long time discussing math in the school library.
A year later I meet another mathematical girl, Tetra. Tetra is one year younger than me, and asks me to teach her math. While I teach her, she begins to understand math and to love its elegance gradually."

The first series is about Fibonacci Numbers, Harmonic Numbers, Finite and Infinite Sums, Factorization, The Basel Problem, Partitions of the Integer, and Generating Functions.

I love math. Just after the high school entrance ceremony, I meet a beautiful girl: Milka. Milka is a mathematical genius. She gives me many math problems, she shows me many elegant solutions. Milka and I spend a long time by discussing math in the school library.

One year later, I meet another mathematical girl: Tetra. Tetra is one year younger than me, and asks me to teach her math. While I teach her, she begins to understand math and to love its elegance gradually.

The second series is about Pythagoras Theorem, Elementary Number Theory, Group, Ring, Field, and Fermat's Last Theorem.

I love math. Just after the high-school entrance ceremony, I meet a beautiful girl: Milka. Milka is a mathematical genius. She shows me many math and many elegant solutions. Milka and I spend a long time discussing math in the school library.

One year later, I meet another mathematical girl: Tetra. Tetra is one year younger than me, and asks me to teach her math. While I teach her, she begins to understand math and gradually to love its elegance.

The third series is about logic puzzles, Peano arithmetic, epsilon-delta, Cantor's diagonal argument, Hilbert's program and Gödel's Incompleteness Theorems.

Ji-ho Seo discovers an abandoned baby that for some reason, is growing up at a rapid rate. Over the course of one year, she will spend with him, what is a lifetime for him.

With tensions between the neighboring country rising signaling the presence of a war soon to begin, Soalla, the princess of a small country, worried whether her own country would be able to defend itself with its weak national power. The king was bedridden and the retainers who were her last rays of hope had nothing but the antiquated motto of battle honor in mind. Not one person had a concrete proposal to protect the country, leaving Soalla to wonder if this was where Favell would fall... However, it was then that Naoki appeared before her. A "magician," that left his name in history who possessed the power she desired to save the country.

That day, I died at the train station and my mind got transferred inside to a body of a girl in a fantasy world.

Kitahara has been having sleeping troubles, yet he's at peace whenever Kuzumi is near.

Hae-Gyeong has a horrible dream in which he meets a terrible group who are killing him saying; "'Boss star' Hae-Deung, the head of Hyeon-Mu! We are here receive your life. Only the universe may know what will be there at the end of this way! Anyhow, you have to die here and now!"
At the offset, it seems that Hae-Gyeong is a very ordinary highschool boy. However, the truth is murkier than even he himself knows... Originally Hae-Gyeong was Hae-Deung, King Hyeon-Mu, in the fantasy world, but his power had been sealed through the veiled enmity caused by his entanglement in the Daegyeolgye causing him to be born into the present world.
Hae-Gyeong is shocked and disbelieving when he hears about this truth from his best friend, Wun-Hak. What is worse, Kin Ju-Jak, suddenly appears and attacks Hae-Gyeong, who has not yet awakened, and he is narrowly rescued by Kin Cheong-Ryong who claims to be his ally.
As he gains a better understanding of his previous life, Hae-Gyeong awakens his powers gradually. How is it going to end?

Suzuo's crush refused his confession and told all others about it, caused him being terribly bullied.. On the isolate island, when Suzuo’s about to commit suicide, the kitten fell from the sky on him!? Being busy to rescue and pamper the weak kitten (Shiro), he forgot to think about dying and was also given a job by the store owner who told about.

Fantasy series of short stories that involves animals:

Pet Doctor Atsushi Kirishima meets a cat-guy with tail, cat ears and an injured eye when he is searching for his runaway patient animal. Atsushi can not leave the cat-guy and takes the guy to his animal hospital with him.

Hattori, an apprentice of Atsushi's father, Kenzou finds a dog in the mountains and brings it back in a car. On the way home the dog changes into a girl.

The titles stories are:

The Sounds of a Bell Can Be Heard
The Cat's Love
A Flicker of Light (two parts)
Amber's Diary (also known as Kohaku's Diary)
The Delicate Pair (also known as Every Subtlety)
(Black Cat + White Dog) > Human

Trouble Little Traveler
A cute unrelated shoujo short story about a boy meeting tiny aliens.

On January 3rd, 2097, a collision with a celestial object basically destroyed human civilization. Seventy years later, human survivors are still living in space, unable to return to their home planet. Some humans, called "Divers" are able to project an avatar to the earth in order to salvage information from earth-based computer networks.

Suzuro is a 14-year-old freelance diver of incredible skill, but only a C-rank due to age restrictions. She works in a salvage ship with her pilot Ginga, who keeps the ship out of flying debris while she's connected to earth, and her assistant Shimugi. It's not only space debris colliding with the ship that could kill Suzuro while diving, there are also dangers waiting on earth that could kill her, just by interacting with her avatar. Suzuro must be certain that the cases she takes are worth the danger!

From Del Rey:
Yamato is ready for a fresh start. So when his aunt invites him to stay rent-free in her big-city boarding house in hustling, bustling Tokyo, Yamato jumps at the chance. There's just one teensy-weensy catch: It's an all-girl housing complex and spa! Things get even more nerve-racking when Yamato meets his neighbor Suzuka, a beautiful track-and-field star. She's not just the cutest girl Yamato's ever met, she's also the coolest, the smartest, and the most intimidating. Can an ordinary guy like Yamato ever hope to win over a girl like Suzuka?

4-koma manga specials included in volumes of Kimi no Iru Machi

IT'S A PURE COMEDY.
The romcom vibe manga，references about anime, film, music and all,
The pretty girl and the handsome guy in the school are auctually 残念, strong-roast: ON

A high-school boy, while sleeping in school, saw a dream in which a girl proposes to him, and then a goddess pops out and grants him something special. The girl from her dream happens to be his classmate sharing the same family name – “Suzuki”. After that, he finds out that he got a special app on his mobile which lets him see other girl thoughts!?

Satou-kun is Peeping(Prequel) it is advised to read it prequel for better understanding of the app.

N/A

Misa Suziki's father wastes all their money being tricked into buying overpriced items to worship gods, or that have special powers. Her mother and father always fight over his constant spending. After Misa makes a wish to the gods, for her parents to stop fighting, her mom decides to go live with her parents. Misa now hates gods, but her god of patron, Ichiro Suzuki, shows up to help her, whom she also hates as a god.

Due to reasons Jinsuke has to live in secrecy with his mother. But they can't stay safe for long. Their pursuers catch up with them, and leave Jinsuke's mother for dead. Their mysterious neighbor Suzuki hears the gun shot, saves Jinsuke, and gets dragged into a murderous chain of events... On the run with the targeted boy, the solitary female assassin Suzuki discovers the warmth of human relationships for the first time.
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