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World map, taken from Kyoukai Senjou no Horizon Volume 1 Part 1.

Countries:

Info is taken partly from the Horizon Wiki (particularly for the pictures) and partly from 境界線上のホライゾンまとめ＠ウィキ. I try to keep spoilers out, while having enough background info to help

The Far East (Kyokutou)
Refers to the land area formerly known as the Divine States (Shinshuu). Composed of the Kantou region, as well as a region south of Tokai (south of Tokyo on the side of the Pacific Ocean). Lost to the Harmonic Divine States in the Harmonic Unification War, and as a result, was put under provisional rule. The entire world was renamed the Far East because of the loss. Though it basically refers to the whole of the Divine States, it is also often used to refer to all those who live outside of the Harmonic Territories - those originally lived in the Divine States - and as a derogatory term.
The primary educational institute is the Musashi Ariadust Academy. The territories of the Far East include Mikawa and Musashi. While most foreign settlements are under the provisional rule from the Testament Union, the Musashi is the sole recognized independent territory.

Hexagone Française (六護式仏蘭西)
A country on the Western Honshu, is under an absolute monarchy at the time of the story, under the Mouri Clan + France. The “Hexagone” (六護式) in the country’s name comes from the fact that the country is shaped like a hexagon. The main academic institution is the Ecole de Paris. Its uniforms are very flashy and, following the renaissance movement from Italy, the lifestyles of the citizenry are becoming more and more secular. As such, it is reflected in the country, now the forefront of fashion. The people are not very stiff or religious, and armaments and knights are becoming less common.
Has custody of Armaments of Deadly Sins, Phuos Kenodoxia (Growth of Vanity) and Phuos Hyperiphania (Growth of Pride); Mouri Terumoto and Louis XIV (Lai Exiv; the “Exiv” comes from the XIV) are the respective owners. Given the Fourth Testament “Prudentitia” (Prudence).

Tres España (三征西班牙)
Located in the Shimoseki region, composed of the Ootomo and Ouchi Clans, and Spain. Also from a merger with Portugal. A country that places importance in having pure-blooded lineage, and is currently in heavy debt. There are many dual-successors. The main educational institution is the Alacalá de Henares.
Has custody of Armament of Deadly Sins, Lypē Katarripsi (Sloth of Lamentation); Tachibana Muneshige is the owner. Given the Sixth Testament “Temperamentia” (Temperance).

M.H.R.R.
Composed of the Hashiba Clan + the Holy Roman Empire, governing the Kinki region.
The Emperor-President, Rudolfini II, is currently under house arrest for the purpose of history recreation. The country has both the Old School (Catholicism) and the New School (Protestant) inside on a very delicate balance. The main educational institution is the A.H.R.R.S. The uniform was not heavily affected by the renaissance period, and as such is based in the knightly and religious culture. However, because of the reformation, the design has had to incorporate designs from both the Old and New Schools. This resulted in a black-heavy, serious, and simple design.
Has custody of the Armament of Deadly Sins, Fonikos Gastrimargia (Strike of Gluttony); the official owner is Matthias. Given the Third Testament, “Caritas” (Charity; Japanese = kindness).

P.A.ODA
The Oda Clan + the Ottoman Empire, ruling over Kinki~Todai. Currently in cooperation with the M.H.R.R., in partial secession from the Testament Union, and in an alliance with Mikawa. The primary educational institution is the P.A.M. The uniform is of a lightweight design, taking into account the desert climate. To prevent their shoes from sinking into the sand, all parts of their shoes are hard-pointed, made from technologies that haven’t changed much since the middle ages. If anything, the design is very pragmatic. The badges attached to their clothes are substitute currency, determined by their weight.
An Armament of Deadly Sins was not put in custody of P.A.ODA due to their religion being Murasai (Muslim). Given the Sixth Testament, Fortitudo (Fortitude; Japanese = courage).

K.P.A. Italia
Refers to the Union of the Aki States (Hiroshima) + United Italian Cities. The country located in the Setouchi area. The Pope-Chancellor, Innocentius, is the head of the Old School (Catholicism), and a believer in the religion. The K.P.A.S. (K.P.A. Scuola) is its chief educational institution.
Currently has custody of the Armament of Deadly Sins, Staseis Porneia (Embodiment of Lust); Innocentius is its owner. The country was given the First Testament “Fides” (Faith).

Sviet Russia / Свет Россия (上越露西亜)
Ruled by the Uesugi Clan + Sviet (little) Russia. Located in Hokuriku; not much is known about the country as of writing. It’s a pileup of areas from the Harmonic Divine States, so living there is quite harsh. The primary educational institute is the J.M.K. To emphasize its neutrality, the uniform is white in color. To ensure a tight fit, the gloves are composed of many parts; anchors are installed on the soles of the shoes, for skiing and combat use. While similar to other schools’ designs, the inner suit of the girl’s uniform is its main component, so it has much more insulation, even more than the boy’s uniform.
Has custody of the Armament of Deadly Sins, Maska Orgē (Flash of Anger); the official owner is Malva Voletskaya. Given the Second Testament, “Spes” (Hope).

Qing-Takeda (清武田)
Rules over the Kanto region, composed of the Takeda Clan + China. Elves play a central role; it is a large country with a mobile city-state. Naomasa’s mother country. Not only because of the geography of the country, but also because there are many who want to succeed the throne, and because it is separate from the European countries, where the Testament Union is based, there are many strong warriors who reign. The primary educational institution is the Kagura Academy (CH: Juéluó Academy).

(note: Originally just called Qing/Shin (清) during writing, but was changed to Qing-Takeda right at the last minute)

England (英国)
A country in the vicinity of the Tsushima island, governed by the Fairy Queen, Elizabeth, who reigns over all 4 layers. Each layer is composed of blocks, with landfills at the sides; a blast furnace in the center serves as a counterpart to the own earth’s core, incinerating the garbage from the landfills. There are a great number of different races; so much so that the Union is over 50% non-human. Not only that, but many of them also have connections to pirates. The main educational institution is Oxford Academy; the uniform is a heavy-type design, made with considerations for winged humanoids. The country maintains neutrality with all of the Divine States.
Has custody of the Armament of Deadly Sins, Aspída Philargyria (Greed of Rejection), the official owner being Thomas Shakespeare. The country was given the Fifth Testament “Justitia” (Justice).

Africa Union (アフリカ諸国)
Shimazumi Clan + Africa. A country with a focus on agriculture; has an abundant labor force.

United States of India (印度諸国連合)
The Houjou Clan + India. Sphere of influence is in East~Kantou. The clan is an automaton-based civilization, the best in the world at automatons, and works behind the scenes in every country. The current head is Houjou Ujinao.

Siberia Uncharted Region (シベリア未踏地域)
A area found in the Tohoku region. An area designated by the Testament Union to remain undeveloped for the purposes of history recreation. Furthermore, it is in a very harsh winter; very few non-humans live in the area. Thus, none of the characters introduced are from the area.

New Continent (新大陸)
Refers to Hokkaido. Left undeveloped for history recreation by the Testament Union, and currently under surveillance to watch for any peculiarities.

Savage Continent (未開大陸)
The Shikoku region; development has not been proceeding because it has been designated by the Testament Union to be an undeveloped area. Has a lot of Harmonic Territories*, and is mainly barren. The residents are mostly composed of Silicon-based races.