The word "Rus'" referred initially to a group of Scandinavian Vikings, also known as Varangians, who founded the medieval state of Kievan Rus' in Eastern Europe in the 10th century. The term gradually acquired the meaning of the aforementioned dynastic polity itself, and also the geographic region of its heartlands Kiev, Pereiaslavl' and Chernihiv. "Russia" is a Hellenized rendition of the same word, and "Ruthenia" is its Latinized form. 
Following the decline of Kievan Rus' in the 12th century, its territory fragmented into multiple polities. The northeastern principality of Vladimir-Suzdal played a crucial role in the eventual rise of the Grand Duchy of Moscow, which, by the 14th to 16th centuries, had consolidated power over most of northeastern Rus'. The name "Russia" began to appear in official documents during this time, alongside the older term "Rus'". By the 15th century, Muscovite rulers adopted the title "Grand Prince of all Rus'," signaling their claim over the legacy of Kievan Rus'. The term "Russia" gradually replaced "Rus'", and by the 16th century, under Ivan IV, the state officially became the Tsardom of Russia. Despite this, the term "Muscovy" persisted in Europe, especially in Latin Catholic regions, but "Russia" was increasingly recognized across Northern Europe and the courts of the Holy Roman Empire.
The name "Ruthenia" originated as a Latinized form of "Rus'" and was commonly used in Western European documents to refer to the eastern Slavic lands during medieval times. Over time, the name became more localized, especially after the 19th century, to refer to Carpathian Ruthenia—a region in the northeastern Carpathian Mountains inhabited by Slavs with a Rusyn identity.
Initially, the ecclesiastical title "Metropolitan of Kiev and all Rus'” was used for the head of the church based in Kiev until the metropolitan see moved to Moscow in the 14th century, where it became "Patriarch of Moscow and all Rus'” with the establishment of the Russian Orthodox Church. In contrast, the southwestern regions of former Kievan Rus' adopted the title "Metropolitan of Kiev, Galicia and all Ruthenia", while modern Ukrainian Orthodox churches have shifted to using titles reflecting "Ukraine" instead of "Rus'."
Etymology.
The most common theory about the origins of Russians is the Germanic version. The name "Rus"', like the Proto-Finnic name for Sweden ("*roocci"), supposed to be descended from an Old Norse term for "the men who row" ("rods-") as rowing was the main method of navigating the rivers of Eastern Europe, and that it could be linked to the Swedish coastal area of Roslagen or "Roden", as it was known in earlier times. 
The name Rus' would then have the same origin as the Finnish, Estonian, Võro and Northern Sami names for Sweden: "Ruotsi", "Rootsi", "Roodsi" and "Ruoŧŧa". The local Finnic and Permic peoples in northern Russia proper use the same ("Rus'"-related) name both for Sweden and Russia (depending on the language): thus the Veps name for Sweden and Swedish is "Ročinma" / "Ročin", while in the Komi language spoken further east the etymologically corresponding term "Roćmu" / "Roć" means already Russia and Russian instead.
The Finnish scholar has pointed out that the territory of present-day Uppland, Södermanland and Östergötland in ancient times was known as "Roðer" or "roðin". Thomsen accordingly has suggested that "Roðer" probably derived from "roðsmenn" or "roðskarlar", meaning seafarers or rowers. Ivar Aasen, the Norwegian philologist and lexicographer, noted proto-Germanic root variants "Rossfolk", "Rosskar", "Rossmann".
George Vernadsky theorized about the association of Rus and Alans. He claimed that "Ruxs" in Alanic means "radiant light", thus the ethnonym "Roxolani" could be understood as "bright Alans". He theorized that the name "Roxolani" a combination of two separate tribal names: the Rus and the Alans.
According to the "Oxford English Dictionary", the English name "Russia" first appeared in the 14th century, borrowed from Medieval Latin "Russia," which was in turn a rendition of the Byzantine Greek name for Rus', Ρωσία (Rosía). The word "Ruthenia" originated as a Latin designation of the region its people called "Rus"'. "Rusia" or "Ruthenia" appears in the 1520 Latin treatise "Mores, leges et ritus omnium gentium, per Ioannem Boëmum, Aubanum, Teutonicum ex multis clarissimis rerum scriptoribus collecti" by Johann Boemus. In the chapter "De Rusia sive Ruthenia, et recentibus Rusianorum moribus" ("About Rus', or Ruthenia, and modern customs of the Rus'"), Boemus tells of a country extending from the Baltic Sea to the Caspian Sea and from the Don River to the northern ocean. It is a source of beeswax, its forests harbor many animals with valuable fur, and the capital city Moscow ("Moscovia"), named after the Moskva River ("Moscum amnem"), is 14 miles in circumference.
Danish diplomat Jacob Ulfeldt, who traveled to Russia in 1578 to meet with Tsar Ivan IV, titled his posthumously (1608) published memoir "Hodoeporicon Ruthenicum"
("Voyage to Ruthenia").
Early evidence.
In Old East Slavic literature, the East Slavs refer to themselves as "[muzhi] ruskie" ("Rus' men") or, rarely, ""rusichi"." The East Slavs are thought to have adopted this name from the Varangian elite, which was first mentioned in the 830s in the "Annales Bertiniani". The "Annales" recount that Louis the Pious's court at Ingelheim am Rhein in 839 (the same year as the first appearance of Varangians in Constantinople), was visited by a delegation from the Byzantine emperor. The delegates included two men who called themselves "Rhos" ("Rhos vocari dicebant"). Louis inquired about their origins and learned that they were Swedes. Fearing that they were spies for their brothers the Danes, he jailed them. They were also mentioned in the 860s by Byzantine Patriarch Photius under the name ""Rhos"."
"Rusiyyah" or "Rūs" (روس) was used by Ahmad ibn Fadlan for what was assumed to be Varangians he met by the Volga River, and by the Persian traveler Ahmad ibn Rustah who visited Veliky Novgorod and described how the Rus' exploited the Slavs.
 ;templatestyles src="Template:Blockquote/styles.css" / ;As for the Rus, they live on an island ... that takes three days to walk round and is covered with thick undergrowth and forests; it is most unhealthy... They harry the Slavs, using ships to reach them; they carry them off as slaves and... sell them. They have no fields but simply live on what they get from the Slav's lands... When a son is born, the father will go up to the newborn baby, sword in hand; throwing it down, he says, "I shall not leave you with any property: You have only what you can provide with this weapon."
When the Varangians arrived in Constantinople, the Byzantines considered and described the "Rhos" (Greek "Ῥῶς") as a different people from the Slavs.
The earliest written mention of the word "Rus'" appears in the "Primary Chronicle" under the year 912. When describing a peace treaty signed by the Varangian Oleg of Novgorod during his campaign on Constantinople, it contains the following passage, "Oleg sent his men to make peace and sign a treaty between the Greeks and the Rus', saying thus: [...] "We are the Rus': Karl, Inegeld, Farlaf, Veremud, Rulav, Gudi, Ruald, Karn, Frelav, Ruar, Aktevu, Truan, Lidul, Vost, Stemid, sent by Oleg, the great prince of Rus', and all those under him[.]"
Later, the "Primary Chronicle" states that they conquered Kiev and created what is now called Kievan Rus'. The territory they conquered was named after them as were, eventually, the local people ("cf". Normans).
However, the Synod Scroll of the "Novgorod First Chronicle", which is partly based on the original list of the late 11th Century and partly on the Primary Chronicle, does not name the Varangians asked by the Chuds, Slavs and Krivichs to reign their obstreperous lands as the "Rus'". One can assume that there was no original mention of the Varangians as the Rus' due to the old list predating the Primary Chronicle and the Synod Scroll only referred to the Primary Chronicle if the pages of the old list were blemished.
Other spellings used in Europe during the 9th and 10th centuries were as follows: "Ruzi", "Ruzzi", "Ruzia" and "Ruzari". Sources written in Latin routinely confused the Rus' with the Rugii, an ancient East Germanic tribe related to the Goths. Olga of Kiev, for instance, was called "queen of the Rugii" ("regina Rugorum") in the Lotharingian Chronicle compiled by the anonymous continuator of Regino of Prüm.
Alternate anti-Normanist theories.
A number of alternative etymologies have been suggested. These are derived from the "anti-Normanist" school of thought in Russian historiography during the 19th century and in the Soviet era. These hypotheses are considered unlikely in Western mainstream academia.
Slavic and Iranian etymologies suggested by "anti-Normanist" scholars include:
The name "Rus'" may have originated from the Iranian name of the Volga River (by F. Knauer, Moscow 1901). George Vernadsky has suggested a derivation from the Roxolani or from the Aryan term "ronsa" (moisture, water). River names such as Ros are common in Eastern Europe.
The Russian linguist Igor Danilevsky, in his "Ancient Rus as Seen by Contemporaries and Descendants", argued against these theories, stating that the anti-Normanists neglected the realities of the Ancient Slavic languages and that the nation name "Rus'" could not have arisen from any of the proposed origins.
Danilevskiy further argued that the term followed the general pattern of Slavic names for neighboring Finnic peoples—the "Chud, "Ves, "Perm, "Sum, etc.—but that the only possible word that it could be based on, "Ruotsi", presented a historical dead-end, since no such tribal or national name was known from non-Slavic sources. "Ruotsi" is, however, the Finnish name for Sweden.
Danilevskiy shows that the oldest historical source, the "Primary Chronicle", is inconsistent in what it refers to as the "Rus'": in adjacent passages, the Rus' are grouped with Varangians, with the Slavs, and also set apart from the Slavs and Varangians. Danilevskiy suggests that the "Rus'" were originally not a nation but a social class, which can explain the irregularities in the "Primary Chronicle" and the lack of early non-Slavic sources.
From Rus' to Russia.
In modern English historiography, common names for the ancient East Slavic state include "Kievan Rus", (sometimes retaining the apostrophe in "Rus'", a transliteration of the soft sign, ь), or "Kievan Ruthenia". The term "Kievan Rus'" was established by modern historians to distinguish the period from the 9th century to the beginning of the 12th century, when Kiev was the center of a large state.
Initially, the Rus' lands referred only to the Middle Dnieper region centered on Kiev, and forming a triangle with Pereiaslav, and Chernihiv. The 12th century chroniclers "record princes from Vladimir–Suzdal’ in the Northeast, Novgorod in the North, and Galicia–Volhynia in the Southwest, among others, as going to the Rus’ Land when Kiev is meant." This narrow usage of Rus’ ceased after the Mongols conquered Kiev in the second half of the thirteenth century. The vast polity of Kievan Rus' was subsequently divided by geographical distance into several more distant principalities. The most influential were, in the south-west, Kingdom of Galicia–Volhynia, in the north, the Novgorod Republic, and in the north-east, Vladimir-Suzdal.
Northeast principalities.
In the 14th–16th centuries most of northeastern Rus' principalities were united under the power of the Grand Duchy of Moscow, once a part of Vladimir-Suzdal, and formed a large state. While the oldest endonyms were "Rus'" (Russian: ) and the "Rus' land" or "Russian land" (Russian: ), a new form of its name, "Rusia" or "Russia", appeared in the 15th century, and became common thereafter. In the 1480s Muscovite state scribes Ivan Cherny and Mikhail Medovartsev mention Russia under the name "Росиа"', Medovartsev also mentions "the sceptre of Russian lordship (Росийскаго господства)". In the following century "Russia" co-existed with the old name "Rus' "and appeared in an inscription on the western portal of the Transfiguration Cathedral of the Spaso-Preobrazhensky Monastery in Yaroslavl (1515), on the icon case of the Theotokos of Vladimir (1514), in the work by Maximus the Greek, the "Russian Chronograph" written by Dosifei Toporkov (?–1543/44) in 1516–22 and in other sources.
By the 15th century, the rulers of the Grand Duchy of Moscow had incorporated the northern parts of the former Kievan Rus'. Ivan III of Moscow was the first local ruler to claim the title of "Grand Prince of all Rus'" This title was used by the Grand Dukes of Vladimir since the early 14th century, and the first prince to use it was Mikhail of Tver. Ivan III was styled by Maximilian I, Holy Roman Emperor as and . Later, "Rus'" — in the Russian language specifically — evolved into the Byzantine-influenced form, "Rossiya" (Russia is ("Rhōssía") in