Nominal declension involves six cases – nominative, genitive, dative, accusative, instrumental, and prepositional – in two numbers (singular and plural), and absolutely obeying grammatical gender (masculine, feminine, and neuter). Up to ten additional cases are identified in linguistics textbooks,[1][2][3] although all of them are either incomplete (do not apply to all nouns) or degenerate (appear identical to one of the six main cases) – the most recognized additional cases are locative, partitive and vocative. Old Russian also had a third number, the dual, but it has been lost except for its use in the nominative and accusative cases with the numbers two, three, and four (e.g. два стула "two chairs"), where it is now reanalyzed as genitive singular.
More often than in many other Indo-European languages, Russian noun cases may supplant the use of prepositions entirely.[4] Furthermore, every preposition is exclusively used with a particular case (or cases). Their usage can be summarised as:[5]
nominative (имени́тельный):
main subject;
default case to use outside sentences (dictionary entries, signs, etc.);
prepositions: за '(what) kind of?'; в: 'join the ranks of' (with pl. noun only);
accusative (вини́тельный):
direct object;
some time expressions;
prepositions indicating motion: в 'into, in(ward)', на 'onto (the top of)', за 'behind, after', под 'under';
other prepositions: про 'about', через 'over', сквозь 'through';
genitive (роди́тельный):
possession – 'of' (genitive noun);
numerals and quantifiers;
negated verbs (which take direct objects in Accusative) to indicate total absence;
some time expressions;
prepositions: без 'without', вместо 'instead of', возле 'near', вокруг 'around', впереди 'ahead of', для 'for', до 'before', из 'from', из-за 'because of, from behind', от 'from', кроме 'except for', мимо 'past by', около 'near', после 'after', против 'against, opposite', среди 'among', у 'by', близ 'near', вдоль 'along', вне 'out of, outside', внутри 'inside';
verbs: бояться 'afraid of', достигать 'reach', избегать 'avoid';
adjectives: полный 'full of' (genitive noun);
dative (да́тельный):
indirect object – 'to' (dative noun);
some time expressions;
impersonal clauses: мне холодно – 'I am cold', lit. "to_me (is) cold";
age statements: мне двадцать лет – 'I am 20 (years old)', lit. 'to_me (is) 20 years';
prepositions: по 'on', к 'to(wards)', благодаря 'thanks to';
auxiliaries: нужно or надо 'need/must (to)', можно 'allowed', нельзя 'forbidden';
verbs: верить 'believe', помочь 'help', советовать 'advise', звонить 'call', удивить(ся) 'amaze (self)';
instrumental (твори́тельный):
instrument used in the action or means by which action is carried out – 'by' (I. noun);
logical subject of passive clause: письмо написано Иваном – 'the letter was written by Ivan';
secondary direct object: его считают студентом – 'he is considered (to be) a student';
durational time expressions;
verbs: интересовать(ся) 'interest (to be interested in)', пользоваться 'use', занимать(ся) 'occupy (to be preoccupied with)';
associates of connective verbs: быть 'be', стать 'became', остаться 'remain', казаться 'appear to be', оказаться 'turn out to be';
prepositions of position: за 'behind', перед 'in front of', над 'above', под 'below', между 'between', (вместе) с '(together) with';
adjective: довольный 'pleased by';
prepositional (предло́жный):
prepositions of place: в 'inside', на 'on (top of)';
other prepositions: о 'about', при 'by/of/with';

Definite and indefinite articles (corresponding to the, a, an in English) do not exist in the Russian language. The sense conveyed by such articles can be determined in Russian by context. However, Russian also utilizes other means of expressing whether a noun is definite or indefinite:
The use of a direct object in the genitive instead of the accusative in negation signifies that the noun is indefinite, compare: Я не ви́жу кни́ги ("I don't see a book" or "I don't see any books") and Я не ви́жу кни́гу ("I don't see the book").
The use of the numeral one sometimes signifies that the noun is indefinite, e.g.: Почему́ ты так до́лго? – Да так, встре́тил одного́ дру́га, пришло́сь поговори́ть ("Why did it take you so long?" – "Well, I met one [=a] friend and had to talk").
Word order may also be used for this purpose; compare В ко́мнату вбежа́л ма́льчик ("Into the room rushed a boy") and Ма́льчик вбежа́л в ко́мнату ("The boy rushed into the room").
The plural form may signify indefiniteness: Вы мо́жете купи́ть э́то в магази́нах ("You can buy this in shops") vs. Вы мо́жете купи́ть э́то в магази́не ("You can buy this in the shop").
The category of animacy is relevant in Russian nominal and adjectival declension.[6] Specifically, the accusative has two possible forms in many paradigms, depending on the animacy of the referent. For animate referents (persons and animals), the accusative form is generally identical to the genitive form. For inanimate referents, the accusative form is identical to the nominative form. This principle is relevant for masculine singular nouns of the second declension (see below) and adjectives, and for all plural paradigms (with no gender distinction). In the tables below, this behavior is indicated by the abbreviation N or G in the row corresponding to the accusative case.
Russian uses three declensions:[7]
The first declension is used for feminine nouns ending with -а/-я and some masculine nouns having the same form as those of feminine gender, such as па́па papa or дя́дя uncle; also, common-gender nouns like зади́ра tease are masculine or feminine depending on the person to which they refer.
The second declension is used for most masculine and neuter nouns.
The third declension is used for feminine nouns ending in ь.
A group of irregular "different-declension nouns" (Russian: разносклоняемые существительные), consists of a few neuter nouns ending in -мя (e.g. время "time") and one masculine noun путь "way". However, these nouns and their forms have sufficient similarity with feminine third declension nouns that scholars such as Litnevskaya[8] consider them to be non-feminine forms of this declension.
Nouns ending with -ий, -ия, -ие (not to be confused with substantivated adjectives) are written with -ии instead of -ие in prepositional (as this ending is never stressed, there is no difference in pronunciation): тече́ние – в ни́жнем тече́нии реки́ "streaming – in lower streaming of a river". But if words в течение and в продолжение represent a compound preposition meaning – "while, during the time of" – they are written with -е: в тече́ние ча́са "in a time of an hour". For nouns ending in -ья, -ье, or -ьё, using -ьи in the prepositional (where endings of some of them are stressed) is usually erroneous, but in poetic speech it may be acceptable (as we replace -ии with -ьи for metric or rhyming purposes): Весь день она́ лежа́ла в забытьи́ (Fyodor Tyutchev).

Additional cases
Some nouns use several additional cases. The most important of these are:
Locative (ме́стный): the most common minor case, used after prepositions of location (на, в(о)). With most nouns the prepositional form is used in such instances. When there is a distinct locative, it may match the dative, or may take a unique form. For example, in во рту́ ("in the mouth"), the locative of рот ("mouth") matches the dative form ртy (and thus differs from the prepositional ртe). In в лесу́ ("in the forest"), the locative of лес ("forest") differs from both the prepositional ле́се and the dative ле́сy (the dative and locative are spelt identically but pronounced differently).
Partitive (отдели́тельный), or second genitive: sometimes used instead of the genitive: налить ча́ю (to pour tea) – not налить ча́я.
Vocative (зва́тельный): used in archaic expressions to call or identify a person: Бо́же мой! (My God!). The modern vocative (sometimes called neo-vocative) is used to produce a person's nickname by removing the vowel ending from the affectionate version of the name: Ива́н (general) — Ва́ня (short, affectionate) — Вань (neo-vocative); Мари́я — Ма́ша — Маш. The neo-vocative has no plural form and can only be applied to names frequently used in Russian; rare names (most of them are non-Slavic) do not have affectionate versions and thus no means of forming the neo-vocative.
Caritive (лиши́тельный), used with the negation of verbs: не знать пра́вды (not know the truth) – знать пра́вду (know the truth). This case sometimes is identical to the genitive and sometimes to the accusative.