We are introduced to Toshinari Seki (who is almost exclusively referred to by his last name and as a break from my tradition, I will also refer to him as such), a boy who sits next to Rumi Yokoi, the main narrator for this series. Instead of concentrating in class and listening to what the teacher is teaching, Seki is setting up a domino run on his desk and this is distracting Rumi, enough that she is startled when called to read out a passage from the textbook. Rumi's sudden standing up disturbs the domino run before its completion, but Seki is able to stop the run before it finishes, although he blames her for nearly ruining everything via a hard stare (Seki never talks throughout the series). When Rumi sits back down and sees that Seki has finished the domino run, which includes: a see-saw, an overpass, a rope-way, and a firework. Seki set it going as Rumi watches in horror at waiting for inevitable bang that will go off at the run's completion, however there is no such sound, as the firework is never lit and any explosions are imagined in Seki's mind. After caught not concentrating on the lesson, Rumi tries to shift focus onto Seki, but the domino run has disappeared.

Seki has got some Shogi (Japanese chess) pieces out and has drawn a Shogi board on his desk with an assumed erasable marker, but is not playing Shogi, but instead a story as the Gold General piece (Shogi equivalent of the Queen chess piece) stages a coup and has killed the King and assumed control of the Shogi army. The change in leadership is not seen as legitimate by the other pieces in the army, so the Gold General resorts to making some of the other pieces disappear via trapdoors built into the desk. These scare tactics bring the army back in line, but the opposing pieces have surrounded the army in a circle; ignoring the drawn out board. The Gold General high-tails out of there, but the army is saved by the old King, but collapses and is held down by the the Gold General until Rumi flicks a rubber at it, knocking it flying.

Seki has brought a cloth to class and is using it to wipe down his desk. This, however, is not enough as he has brought out some putty, polishing wax, curing resin, epoxy, distilled water, etc which he uses to polish his desk enough that is basically becomes a mirror. He then intends to do the same to Rumi's desk and is willing to pay 500 yen (about £2.40), however she refuses. Seki is very insistent, so Rumi compromises and offers her pencil board for him to polish instead. After some fervent polishing, Seki returns Rumi's pencil board/ now impromptu mirror, but both their hair stands up thanks to all of the static electricity generated, much to Rumi's annoyance.

Seki has poured sand on his desk and places a flag on top of the mound of sand that forms. Rumi assumes he is playing a version of 'Topple the Pole' (Bo-taoshi) a game where 2 teams of 150 each (split in 2 groups of 75: offence and defence) try to knock the opposing team's pole down 30 degrees with the defending forming a sort of human pyramid around their pole and the attacking team clambering over. This version obviously replaces the people with sand as the attacking player tries to remove sand to knock the flag down while the defending player attempts to put sand back to right the flag. After removing some sand, Seki begins to spray what's left with water to harden the sand and begins to chip away at the sand whilst also spraying the sand in an effort to maintain its rigidity. He finishes with a long thin column of sand and places some miniature 'keep out' fencing around it. Seki is then called to solve a problem at the front of the class so slowly and gingerly tries to get up, but is taking too long so Rumi is called instead and her getting up is too quick and the subsequent shock-waves generated causes the sand column to collapse, which angers Seki and Rumi si angry back because she did nothing wrong an all of this could have been avoided if he was studying and properly concentrating on the class like a proper student.

Seki has got some Go pieces out but isn't playing a one-player game of it, instead he has created a teddy bear and and a rabbit and has them wrestle each other. The teddy bear and the rabbit must have performed the fusion dance during their wrestling match as the 2 fuse to become a teddy-rabbit, which then fights a palette-swapped version of itself (what is black on teddy-rabbit is white on the palette-swap and vice versa). These fights distracts Rumi enough that she is noticed by her teacher and tries to explain that it was all Seki's fault, but all the evidence she has is a drawing she drew in her notebook of the teddy bear and the rabbit wrestling each other.

Seki has brought a cat to class today and is petting, much to Rumi's frustration as she too wishes to pet the cat as after all, it is SO cute. Unfortunately for Rumi, Seki doesn't seem to be willing to share the cat even if he pulls another one from somewhere and has it on his lap. Rumi tries to entice this cat by waggling her ruler in front of it, but Seki has a foxtail toy which is far more interesting. Rumi remembers she has fried shrimp as a part of her lunch and attempts to entice a cat with it, but Seki is already feeding them some small fish. Seki then notices a depressed a Rumi and points at her, which she interprets as him offering her a cat, but he is instead offering her a fish

Rumi notices letters being sent across the class, with Seki having a lot of them as well as stamping them. Seki then hands her a letter which has come from her friend Tomoka Hashino, who explains that Seki is running a postal service and eagerly awaits her reply. Rumi writes a letter to Seki, but it is rejected for being of irregular size. She then resizes her letter to be the correct size, but Seki's post office is now closed and she has to put her letter through the letter box that he has set up at the back of the classroom. She can just about reach it, but it requires her lean far enough back on her chair that it falls over. Seki goes home without ever emptying the letterbox, so Rumi puts her letter in his shoe locker, inciting weird rumours.

Seki is playing with chess pieces and has stacked all of the black pieces into one massive piece. Seki then moves the massive piece around, crushing the white pieces to bits. One of the white knight pieces has managed to make it to the top of the black piece megastructure, but suffers the same fate as many of its fellow coloured pieces as the black mega-piece spins around, swallowing the knight and breaking it to smithereens on its journey down. Rumi then flicks some of the shards that were the knight at Seki's desk, knocking 2 white pawns over which get caught underneath the black mega-piece and loses its balance and falls off his desk.

Rumi is the first one in the classroom and takes advantage of the situation by investigating Seki's desk. Inside are boxes labelled with seasons and then subtitled with a weight descriptor. She opens a box up and inside are bottles which are labelled with a date range and descriptor that describes where it was found or what is like. Rumi decides to put them back, but the bottles won't fit and then someone else enters the classroom, forcing Rumi to hide in an effort not to be caught with Seki's stuff and incite weird rumours again. Rumi tried to put the boxes back, but they too don't fit, so puts them in her desk, as more and more people are entering the classroom; including Seki. However, one of the boxes begins to rustle as she put it away.

After being hit by a tennis ball during P.E, Rumi takes a break on the sidelines, where she notices Seki has a line marker and is not participating in the lesson either. She begins to follow but encounters the word "Stop" on the ground that Seki has drawn. She ignores the sign and follows Seki where has drawn a "Do Not Enter" sign, complete with diagonal lines. She skips over these and then encounters some cat faces, some of which are too cute to step on. Some, however, are not cute so she is willing to step on them. She navigates her way out of the cat face maze but it ends outside the teacher’s faculty room which is full of teachers and one of them gives stern talking to Rumi and demands she clean up her ‘mess’.

Seki is making some origami animals, starting with a crane. Rumi predicts that he’ll make some other animals and have them fight to the death, but she is wrong as he makes more cranes. She then assumes that the cranes will merge into one mega-crane, so tries to ignore what he doing as her curiosity satisfied. However, he still making cranes with such seriousness that she assumes that he is making 1,000 of them for someone that is sick (something Japanese people do for sick people) and probably that person is someone that he knows, so she also makes some origami cranes as well using his origami paper. With 1,000 cranes made, Rumi is satisfied with doing a good turn, while Seki makes a large origami frog that ‘eats’ the cranes, which angers Rumi and she blows the origami animals away using her notebook.

It's a science lesson but Seki is more interested in pseudosciences as he has brought out an Ouija board and begins a session. A fellow classmate, Uzawa, decides to join in the session (a big no-no apparently) which causes Seki to tense up significantly as he is a big believer (or fear-er) in the occult. Uzawa decides that they should ask the spirits what the name is of the girl Seki likes, but we only get as far as the first syllable as Uzawa gets bored and leaves the session (another big no-no). Seki is going mad from fear and stress and signals to Rumi to get him his bag as he would need to leave the Ouija session to do that and that would release all manner of curses upon everyone (probably). Rumi hands him his bag and he gets out an offering for the spirits which should placate them. Uzawa spots this and decides to take one of the offerings as the offerings are food but doesn't notice the decoration that indicate it might be for someone on the other side.

Seki is knitting in class, which piques Rumi's interest as she is an expert at knitting (she is a 2nd-rank licensee of the Knitting Society). Seki's knitting speed impresses her, but he is only doing the most basic of crochets. The narrow stitching and cotton stuffing indicates he is making a stuffed toy (a Amigurumi to be exact), but he is using a Double-Ended Afghan hook, which is used making Afghan clothes which are known for their bumpy texture and Amigurumis need to be smooth to appealing. However, Seki is making a Cactus and the bumpy nature of Afghan knitting helps accentuate coarseness of a cactus' skin. Rumi accepts that Seki knows what he is doing and as a consolation prize, wishes to cuddle the Cactus, but Seki interprets her signs differently and unravels the cactus. This angers Rumi, who indignantly stares at him to remake the cactus, but Seki too scared by her stare to do anything that but hold a textbook.

The school is having a disaster drills which they want the students to take seriously, except Seki is more interested in playing with a family of robot action figures and has them set up in a living room on his desk. An announcement comes over the tannoy that there's an "earthquake" and everyone (except Seki) gets underneath their desks and the robot family hide under their living room coffee table (or for Dad-bot, a large cushion). Once the "earthquake" has stopped everyone evacuates to the school-yard in an orderly fashion and the robot family tag along too in Seki's jacket pocket, which is visible to Rumi as he has his jacket in hand and is very laissez-faire about the whole thing which annoys Rumi. As the students are given a speech about the importance of these drills, Seki is too busy chatting away with his friends to notice he accidentally knocks the robot family and Rumi takes it upon herself to rescue the family and looks after them for rest of the day, playing with like Seki would.

The class has music and the classical music being played is putting everyone, including the teacher, to sleep; except for 2: Rumi and Seki. Seki is keeping himself awake my playing with a jigsaw puzzle, while Rumi keeps herself awake through sheer determination and a will to not lose to Seki and is willing to use stimulants (a mint sweet) to succeed. Seki sees her with the sweet in her hand and the stare he gives convinces Rumi to continue on without eating the sweet, but ends up falling asleep. Now the only one awake, Seki has now made 2 pyramids out of jigsaw pieces and then slams down a caffeine energy shot and gets to work making a sphinx as well.
There are 2 bonus chapters with the first on in 2 parts and focuses on characters in the series interacting with Seki. The 1st part is Maeda, a class mate of Seki's, testing a new pitch throw that suggested to by Seki, but wondering if he should use it. The 2nd part revolves around 2 teachers with one explaining why he has to reject club ideas that Seki has come up with, with his colleague eventually coming to same conclusion.
The 2nd bonus chapter is autobiographical as is sees Takuma Morishige discovering a high-tech whiteboard at the editorial office of Comic Flapper (the Japanese magazine which serialised My Neighbour Seki) and showing it off to his Editor who has never see it ever used.