Kids on the Slope

Sakamichi no Apollon is a Manga series by Yuki Kodama.

Summer, 1966. Kaoru Nishimi (Ryouhei Kimura) constantly moves from town to town and school to school due to his father's job. Because of his intelligence, his wealthy background, and his nausea problems, Kaoru has been alienated by his classmates and is subsequently seen as an outcast. When Kaoru transfers to yet another school, this time in Kyushu, he expects the same things to happen as they always do. However, this time his luck begins to change as he meets seeming Delinquent Sentarou Kawabuki (Yoshimasa Hosoya) and pretty class president Ritsuko Mukae (Yuuka Nanri), and the trio begin bonding over Jazz music.

The series won the 57th Shogakukan Manga Award for general manga and has been adapted to an anime for the Spring 2012 Anime season, airing on the Noitamin A block. The anime adaptation is notable for being directed by Shinichiro Watanabe and music composed by the acclaimed Yoko Kanno.

This series contains the following tropes:

 * Animation Bump: The anime's musical sequences.
 * Beach Episode: Chapter 5/Episode 2.
 * Big Brother Mentor: Junichi.
 * Blind Without Em: Averted. Kaoru frequently takes off his glasses, usually to impress Ritsuko. One Impairment Shot shows that he's a bit myopic, but can see well enough to get around.
 * Bratty Half Pint: Kaoru's cousin Mariko, who asks Kaoru to play the piano in the morning, only to blame him and get him in trouble when his aunt catches him.
 * Broken Pedestal:, as of Episode 8.
 * Butt Monkey: Maruo.
 * Childhood Friends: Sentarou and Ritsuko.
 * Coming of Age Story
 * Conspicuous CG: Kaoru's thrown umbrella and piano-playing hands.
 * Creepy Cool Crosses: Sentarou wears a rosary around his neck. Kaoru is surprised by this, and Ritsuko mentions that it's uncommon, but the priest allows only Sentarou to do this. Sentarou quickly ends the conversation, and for a second Kaoru senses there was a different atmosphere.
 * Dark and Troubled Past: Sentarou.
 * Delinquent: Sentarou comes off as this and doesn't really help his case when he ends up in fights.
 * Dogged Nice Guy: Kaoru towards Ritsuko, and Sentarou towards Yurika.
 * Face of a Thug: Sentarou.
 * The Faceless: The eyes of Yurika's parents are never shown.
 * First Name Basis: Sentarou and Ritsuko call each other by their first names and are familiar with each other because they are Childhood Friends. Ritsuko offers Kaoru to call them by their first names as well.
 * Genki Girl: Ritsuko.
 * Girlish Pigtails: Ritsuko.
 * Gratuitous English: Sentarou's rock band at the culture festival is named "The Olympus". There's a brief dispute over whether to adapt "the" as "ji" or "za" (which imitate either pronunciation of "the").
 * Green Eyed Monster:
 * Hair Decorations: Ritsuko.
 * Heterosexual Life Partners: Kaoru and Sentarou.
 * Idiosyncratic Episode Naming: Jazz song titles
 * Imaginary Love Triangle:
 * By the end of the first volume, Kaoru, who has feelings for Ritsuko, questions the nature of Sentarou's and Ritsuko's childhood friendship and suspects that there might be something between them or that one might like the other. He eventually comes to the conclusion that he just was over-thinking things
 * Important Haircut: Sentaro has one in the flashback, shortly after he gets into his first fistfight over being only half-Japanese.
 * Yurika cuts her hair in front of Junichi, in an attempt to stop being The Ojou.
 * In Series Nickname: Ritsuko is referred to by Kaoru as "Ricchan" and by Sentarou as "Rikko," and Sentarou refers to Kaoru as "Bon" (short for "Bonbon-dono"), which is the Kansai dialect for a green or naive man from a well-to-do family. Both official subs naturally adapt this to "Richie".
 * Indirect Kiss: In Chapter 5/Episode 2, Sentarou asks Kaoru for a bite of the latter's ice cream. Kaoru declines, so Ritsuko offers hers; Kaoru, realizing that that would be an indirect kiss, hastily offers his ice cream instead.
 * Intelligence Equals Isolation: One of the factors that alienates Kaoru from his classmates. When he recites a passage in fluent English, one of his classmates mutters disdainfully that he's showing off.
 * Japanese Christian: Sentarou and Ritsuko, to Kaoru's surprise.
 * Jazz: What the series revolves around.
 * Josei
 * Last Name Basis: You can tell Kaoru's really in a rough patch when he reflexively reverts to "Mukae-san" to declare "She Is Not My Girlfriend".
 * Love Dodecahedron:
 * Love Hurts
 * Luminescent Blush: Kaoru towards Ritsuko; Sentarou towards Yurika.
 * Meet Cute:
 * Kaoru/Ritsuko. Kaoru is staving off his nausea, but seeing her makes it miraculously go away.
 * Kaoru/Sentarou. Kaoru removes a sheet from some chairs to find a sleeping Sentarou by accident, who, still half-asleep, takes Kaoru's hand and tenderly says, "So you finally came for me?"
 * Sentarou/Yurika. Sentarou rescues Yurika from boys who were harassing her.
 * Megane: Kaoru.
 * Mythical Motifs: See title. Yurika uses Sentarou as a model for Apollo in a painting. The story's All Love Is Unrequited plot is also compared to the tale of Apollo and Daphne. Additionally, Sentarou joins a temporary rock band called the Olympus for the culture festival in second year.
 * New Transfer Student: Kaoru frequently transfers schools due to his father's job.
 * Nice Job Breaking It Hero: Kaoru's attempt to help Sentarou get closer to Yurika results in
 * Not What It Looks Like:
 * Parental Abandonment: Kaoru's father is usually away because of his job on a ship, and Kaoru's mother left him at a young age.
 * Red Oni Blue Oni: Sentarou and Kaoru.
 * Technician Versus Performer: Kaoru starts off with classical piano training but Sentarou slates his rendition of "Moanin'" as lacking "swing."
 * Red String of Fate: The anime's ending theme is about unrequited love, which is probably why the sequence extrensively uses imagery of a blue string.
 * Rich Bitch: Kaoru's aunt.
 * Scenery Porn: In the Anime.
 * Shipper On Deck: Several girls in Kaoru and Ritsuko's second year class try to push them toward each other.
 * Slice of Life
 * Surprisingly Good English: In episode 4, the drunk American speaks English very well, and at a reasonable speed.
 * Tall Dark and Bishoujo: Yurika.
 * Three Amigos: Kaoru, Sentarou, and Ritsuko.
 * Two Guys and A Girl
 * Vitriolic Best Buds: Sentarou and Kaoru have a more downplayed version of this dynamic. Ritsuko also compares their improv performance at the culture festival to this trope.
 * Tall Dark and Bishoujo: Yurika.
 * Three Amigos: Kaoru, Sentarou, and Ritsuko.
 * Two Guys and A Girl
 * Vitriolic Best Buds: Sentarou and Kaoru have a more downplayed version of this dynamic. Ritsuko also compares their improv performance at the culture festival to this trope.