Russia is the most poliglot country of the world
80 languages only in European Russia

Background

Before the dissolution of the Soviet Union in the early 1990's, the population of the USSR was approximately only half Russian-speaking, and the percentages of Slavic speakers was declining. Even if Ukrainian, Belorussian and other Indo-European languages added, still a large proportion of the population spoke Altaic (Turkic, Mongolian etc.), Caucasian (two families) and other non-Indo-European languages. Demographic trends indicated their percentages would increase.

Before the Soviet Revolution (1917) only Russian was an official language, but some of the "Christianized" groups (Armenians, Georgians, Baltic peoples, Finns?) used their own languages and had for some time. Other groups' languages were not reduced to writing, or had been used for limited purposes; the Muslim populations of Central Asia and some of the Caucasus may have used Arabic or their own languages with Perso-Arabic script, but literacy was very limited. Poles, Ukrainians and Belorussians were not so lucky; the plan was to russify them, increasingly in the late 19th century.

The revolutionary policy (10th Congress, 1921) abandoned russification and proceeded to implement the pluralist policy, but reserving a role for Russian, as centrist meaning that it would be the lingua franca, the language used by the military, in meetings of the Supreme Soviet, by the central government, etc. The national languages would be used at the periphery, in territories set up for them. Much discussion was made about russification, even ongoing russification in the RSFSR (the Russian Republic) of Ukrainian etc. minorities, but it was clear from the start that a tension between the two would always exist, and that even when russification was under attack, it would covertly continue to exist, and would surface from time to time. Russian language in particular would struggle against "national culture" (i.e. too much regional power, regional language) which was "bourgeois". Nations were eventually to be abolished, and people would live without nationalism (a bourgeois concept) in peace and harmony; and this would be done, within the USSR, with Russian. Russian was therefore, in some sense, "neutral", i.e. not an ethnic language.

Other aspects of the role of Russian were that Russian had always been the lingua franca, especially in the army, where men had been conscripted and had somehow learned it.

Russian loan words had penetrated other languages.

Science and technological progress would come through Russian and Russians would be primus inter pares

Nowhere is it stated, but in effect Russian has `personal status in the USSR (whereas ethnic languages only had territorial) because Russian was fully portable ; wherever Russian speakers went, their linguistic rights would be guaranteed, and they would never have to learn another language.

Bilingualism before the RR: there was much bilingualism, especially among men (army etc.) and some groups were more bilingual than others, e.g. Jews and Germans, who had no territory of their own (unlike Kazakhs or Latvians). Other groups, especially small ones, had sometimes been bilingual in other languages, eg. Mingrelians in Georgian, Poles in Lithuanian, Finns in Estonian or Swedish, etc. But the lingua franca had been mostly Russian. (For a discussion of the current situation in post-Soviet Latvia

In present days there nearly 200 languages spoken in Russia, of which about 80 are spoken in the European (western) republics of the Russian Federation.

In this article we will deal only with languages spoken in European Russia.

There are 80 different languages with populations varying from a few hundred speakers to several million.

We will deal specifically with the languages with the largest number of speakers (more than 100,000) and merely list the remaining ones.

1 Russian  The main language of Russia which is the official language and the lingua franca of the Russian Federation is Russian with 150 million native speakers.

2 Tatar

After Russian, the language with the most speakers of the federation is Tatar. There are 6,500,000 speakers of the Tatar language.

Tatar is a Turkic language spoken by Tatars mainly located in modern Tatarstan (European Russia).. Tatarstan is a republic of the Russian Federation. It is located in the Volga Federal District and its capital is Kazan. It is spoken by 6,500,000 people.

3 Chuvash  

Chuvash is also a Turkic language spoken in the Chuvash Republic and adjacent areas. It is the only surviving member of the Oghur branch of Turkic languages. The Chuvash Republic is located in the center of European Russia, in the heart of the Volga-Vyatka economic regiona, mostly to the west of the Volga River in the Volga Upland. It is spoken by 1,640.000 people.

4 Bashkir   

Bashkir is a Turkic language belonging to the Kipchak branch. is It is co-official with Russian in Bashkortostan.  It is spoken by approximately 1.2 million native speakers. It is spoken by approximately 1.2 million native speakers, it is a republic of Russia.It is located between the Volga River and the Ural Mountains Its capital is the city of Ufa. With a population of 4,072,292 as of the 2010 census, Bashkortostan is the most populous republic in Russia. It is spoken by 1,450,000 people.

5 Chechen

Chechen is a  Northeast Caucasian language spoken by more than 1.4 million people, mostly in the Chechen Republic and by members of the Chechen diaspora (750,000)

6 Avar, 

It is calle "language of the mountains") or "Avar language"), also known as Avaric, is a language that belongs to the Avar-Andic group of the Northeast Caucasian family primarily spoken in Dagestan. Dagestan is a federal republic of Russia , located in the North Caucasus region. Its capital and largest city is Makhachakala centrally located on the Caspian Sea coast . With a population of 2,910,249 Dagestan is very ethnically diverse and Russia's most heterogeneous republic, with the largest ethnicity constituting less than 30% of the population. There are approximately 784,000 Avar speakers.

7 Kabardian

 also known as Kabardino-Cherkess (къэбэрдей-черкесыбзэ) or East Circassian, is a Northwest Caucasian language closely related to the Adyghe. It is spoken mainly in parts of the North Caucasus republics of Kabardino-Balkaria and Karachay-Cherkessia (Eastern Circassia) and in Turkey, Jordan and Syria. There are 587,000 Kabardian speakers..

8 Darkwa 

The Dargwa language is spoken by the Dargin people in the Dargin republic of Dagestan. It is the literary and main dialect of the dialect continuum constituting the Dargin languages. There are about 503,000 Darkwa speakers.

9 Ossetic

It is an Eastern Iranian language spoken in Ossetia in the northern slopes of the Caucasus Mountains. It is a relative and possibly a descendant of the extinct Scythian, Sarmatian and Alanic languages.

The Ossete area in Russia is known as North Ossetia-Alania, while the area south of the border is referred to as South Ossetia, There are about 493,000 Ossetic speakers.

10 Udmurt

It is a language of the Permic subgroup, spoken by the Udmurt natives of the Russian constituent republic of Udmurtia, where it is co-official with Russian. It is written using the Cyrillic alphabet. There are about 463,000 Udmurt speakers.

11 Kumyk 

It is a Turkic language, spoken by about 426,212 people. The Kumyks inhabit Dagestan, North Ossetia and Chechen republics of the Russian Federation.

12 Eastern Mari

The Mari language (spoken by approximately 400,000 people, belongs to the Uralic language family. It is spoken primarily in the Mari republic of the Russian Federation as well as in the area along the Vyatka  river basin and eastwards to the Urals. Mari speakers, known as the Mari also in the Tatarstam, There are bout 451,000 speakers

13 Ingush

is a Northeast Caucasian language spoken by about 500,000 people, known as the Ingush, across a region covering the Russian republics of Ingushetia and Chechnya.

14 Lezgian

Lezgian  is a Northeast Caucasian language that belongs to the Lezgic languages with 397,000 speakers.

It is spoken by the Lezgins, who live in southern Dagestan, northern Azarbaijan, Turkmenistan, Uzbekistan, Kazakhstan, Turkey, Germany and other countries. Lezgian is a literary language and an official language of Dagestan.

15 Karachay-Balkar

is a Turkic language spoken by the Karachays and Balkars in Kabardino-Balkaria and Karchay-Cherkessia, Eastern Russia, as well as by an immigrant population in Afyonkarahisar Province, Turkey, Spoken by 302,000 people.

16 Komi-Zyrian 

It is one of the two regional varieties of the pluricentric Komi language. The other regional variety being Komi-Permyak..

Komi-Zyrian is spoken by the Komi-Zyriangs ethnic group in Komi Republic and some other parts of Russia. There are about 250,000 speakers.

17 Kalmyk

Kalmyk is part of the Oirat language branch, natively spoken by the Kalmyk people of Kalmykia, a republic of Rusia. It is the standard form of the Ourai language based on the Torgut dialect), which belongs to the Mongolic language family. The Kalmyk people of the northwest Caspian Sea of Russia claim descent from the Oirats from Eurasia. There are 153,000 Kalmyk speakers.

18 Lak 

Lak is the language of the Lak people from the Russian autonomous republic of Dagestan, where it is one of six standardized languages. It is spoken by about 157,000 people.

19 Adyghe  

Adyghe is also known as West Circassian. It is one of the two official languages of the Republic of Adygea in the Russian Federation, the other being Russian. It is spoken by various tribes of the Adyghe people: Abzekh, Ademay, Bzhedug, Hatuqwai, Temirgoy, Amkhegh, Nagekuay, each one with its own dialect.

The language is referred to by its speakers as Adygebze or Adəgăbză.

There are 129,000 Adyghe speakers 

20 Tabassaran 

Tabassaran is a Northeast Caucasian Language of the Lezgic branch. It is spoken by the Tabasaran people of the Russian Republic of Dagestan. There are two main dialects: North (Khanag) and South Tabasaran. There are 128,000 Tabassaran speakers.

Other languages

To these languages we will add 32 others with less than 100,000 speakers.

In the following list we transcribe the name of those languages and their number of speakers.

Abaza 38,000

Western Mari 36,000

Kurmanji 30,000

Yiddish 30,000

Rutul  29,000

Rutul 29,000

Aghul  29,000

Andi 23,000

Baltic Romany 20,000

Tsez 15,000

Bezhta 10,000

Vlax Romany 10,000

Mordovian languages 40,000

Livvi (no data)

Assyrian Neo-Aramaic 7,700

Khwarshi  3,000

Serbian

Veps

Tindi

Karata

Ludian

Hunzib

Bagvalal

Botlikh

Tsakhur

Akhvakh

Ghodoberi

Archi

Chamalal

Judeo-Tat

Languages with fewer than 1,000 speakers

Sami languages

Vod

Ingrian

Hinukh

And 15 languages that are official in other countries:

English  7,574,302

German  2,069,949

Ukranian 1,300,000

Armenian 904,000

Azerbaijani 669,000

Beñarissian 316,000

Georgian 286,000

Turkish  161,000

Romanian 147,000

Polish 94,000

Finnish  51,000

Lithuanian  49,000

Latvian 34,000

Estonian 26,000

Serbian

Baltic Romani

Yiddish

That is 79 languages in European Russia, plus Russian=  80 languages

References:
https://www.sas.upenn.edu/~haroldfs/540/handouts/ussr/soviet2.html
https://en.wikipedia.org/wiki/Languages_of_Russia