Russian declension

In Russian grammar, the system of declension is elaborate and complex. Nouns, pronouns, adjectives, demonstratives, most numerals and other particles are declined for two grammatical numbers and six grammatical cases ; some of these parts of speech in the singular are also declined by three grammatical genders. This gives many spelling combinations for most of the words, which is needed for grammatical agreement within and outside the proposition. Also, there are several paradigms for each declension with numerous irregular forms.
Russian has retained more declensions than many other modern Indo-European languages.

Nouns

Nominal declension comprises six cases – nominative, accusative, genitive, prepositional, dative, instrumental, two numbers, and three grammatical genders. Up to ten additional cases are identified in linguistics textbooks, although all of them are either incomplete or degenerate. The most recognized additional cases are locative, partitive, and several forms of vocative. The adjectives, pronouns, and the first two cardinal numbers further vary by gender. 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.
Russian noun cases often replace the usage of prepositions in other Indo-European languages. Their usage can be summarised as:

Nominative – the “subject” case
Accusative – the “direct object” case
Genitive – corresponding to the possessive case or “of + ”
Prepositional – used with certain prepositions, such as “in”, “on” etc.
Dative – corresponding to “to + " or the indirect object
Instrumental – denoting an instrument used in an action

There are no articles, neither definite nor indefinite, in the Russian language. The sense of a noun is determined from the context in which it appears. That said, there are some means of expressing whether a noun is definite or indefinite. They are:

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" and "Я не ви́жу кни́гу".
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".
Word order may also be used for this purpose, compare "В ко́мнату вбежа́л ма́льчик" and "Ма́льчик вбежа́л в ко́мнату".
The plural form may signify indefiniteness: "Вы мо́жете купи́ть э́то в магази́нах" vs. "Вы мо́жете купи́ть э́то в магази́не".

The category of animacy is relevant in Russian nominal and adjectival declension. Specifically, the accusative has two possible forms in many paradigms, depending on the animacy of the referent. For animate referents, 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 and adjectives, and for all plural paradigms. In the tables below, this behavior is indicated by the abbreviation N or G in the row corresponding to the accusative case.
In Russian there are three declensions:

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 "papa" or "uncle"; also there are common-gender nouns like "teaser" which are masculine or feminine depending on the person they refer to.
The second declension is used for most masculine and neuter nouns.
The third declension is used for feminine nouns ending in ь.

There is also a group of several irregular "different-declension nouns", consisting of a few neuter nouns ending in -мя and one masculine noun "way". However, these nouns and their forms have sufficient similarity with feminine third declension nouns that some scholars such as Litnevskaya consider them to be non-feminine forms of this declension, as written in the tables below.
Nouns ending with -ий, -ия, -ие are written with -ии instead of -ие in Prepositional: тече́ние – в ни́жнем тече́нии реки́ "streaming – in lower streaming of a river". But if the words and are representing compound prepositions meaning "while, during the time of", they are written with -е: в тече́ние ча́са "in the course of an hour". For nouns ending in -ья, -ье, or -ьё, using -ьи in the Prepositional is usually erroneous, but in poetic speech it may be acceptable : Весь день она́ лежа́ла в забытьи́.

First declension

The first declension group belongs to nouns with the ending -а and -я. These nouns are typically feminine, but include masculine nouns that have a feminine ending as well.

After a sibilant or a velar consonant, и is written.
After a sibilant, о is written when stressed; е when unstressed.
After a soft consonant, ё is written when stressed; е when unstressed.

Examples:
рабо́та – a work/job, ба́ня – a bathhouse, кни́га – a book, ли́ния – a line
Note: In the instrumental case, -ою and -ею instead of -ой and -ей endings may be encountered in the singular.

Second declension – masculine nouns

Nouns ending in a consonant are marked in the following table with –.
Notes:

After a sibilant or a velar consonant, и is written, or, for some words, а.
After a sibilant, ей is written.
After a soft consonant, ё is written when stressed; е when unstressed.
After a sibilant, о is written when stressed; е when unstressed.

Examples:
фильм – a film/movie, писа́тель – a writer, геро́й – a hero, коммента́рий – a comment

Second declension – neuter nouns

Nouns ending in -о and -е are neuter.

After a sibilant, о is written when stressed; е when unstressed.
After a soft consonant, ё is written when stressed; е when unstressed.
For nouns ending in ие in the nominative singular, и is written.
After a consonant use ей otherwise use й.
Also: some masculine nouns ending in -о in the nominative singular ; there is only one masculine noun ending in -е in this declension: Journeyman.

Examples
ме́сто – a place, мо́ре – a sea, зда́ние – a building

Third declension

The third declension is for predominantly feminine nouns, or with a non-standard termination as shown with exceptional words: дитя and путь.

After a sibilant, а is written.

Examples:
кость – a bone, мышь – a mouse, и́мя – a name

Irregular plural forms

There are various kinds of irregularities in forming plurals. Some words have an irregular plural form, but a few use suppletion, being substituted by a different root altogether. Historically, some of these irregularities come from older declensional patterns that have become mostly obsolete in modern Russian.

If the word лист has the lexical meaning "sheet ", then its declension is normal. If it has lexical meaning "leaf ", its declension is лист → лист.
Indeclinable nouns

Some nouns are not modified when they change number and case. This appears mostly when their gender appears to have no ending in any declension which suits the final part of the word: these are masculine names on vowels different from -а/-я, female names on hard consonants. Most borrowed words ending in Russian in э/е, и, о, у and stressed а are not declined: Café, overcoat, Dumas etc. Most abbreviations are undeclined. The name Bangladesh is also undeclined, despite ending on a consonant.
Many people also think that Georgian surnames on -ия like Данелия shouldn't be declined since they are originally something like Russian possessive genitives.

Personal names

Traditionally, a full Russian name consists of a person name, patronym and a family name. All of these words have the same grammatical gender as biological one. Slavic, as well as Greek, Roman, Jewish and other person names of European or Semitic origin loaned centuries ago, have gender-specific versions of respective patronyms. To produce a patronym, suffixes -вич- and -вн- are used with final vowel addition or modification: -о for hard consonant, -ье for -ий, and -е for other cases. Some person names also have versions for both males and females.
Additionally, Slavic names have short forms, usually meant for affectionate calls. Short forms by themselves can form "reemerging" vocative case ; it is used for calling a familiar person, substituting nominative singular by removing last vowel. For this reason, neo-vocative is not possible for male names that can't produce short forms with a final vowel. Likewise, there is a neo-vocative form for close relatives: мать – ма́ма – мам, оте́ц – па́па – пап. When replacing nominative plural, it can be used for collective calls: ребя́та – ребя́т, девча́та – девча́т.
Most family names in Russia are also gender-specific and declinable like most words. They can be divided in these categories :

Russian origin, gender-specific, declinable as nouns: -о́в/-о́ва, -ев/-ева, -ёв/ёва, -и́н/-ина́ ;
Russian origin, gender-agnostic, indeclinable: -ы́х, -и́х;
Ukrainian origin, gender-specific, declinable as adjectives: -ый/-ая, -о́й/-а́я;
Ukrainian or Belarusian origin, gender-agnostic, indeclinable: -е́нко, -ко́;
Ukrainian or Belarusian origin, gender-agnostic, declinable as masculine nouns for males and indeclinable for females: -у́к, -ю́к, -и́к, -е́ц, etc.;
Other Slavic origin, gender-specific, declinable as adjectives: -ский/-ская, -цкий/-цкая;
Other Slavic or non-Slavic origin, gender-agnostic, declinable as masculine nouns for males and indeclinable for females: -о́вич, -е́вич, -ер, -ман, -берг, etc.

Examples:

	male	female	family or couple
Nominative	Ю́ри	Валенти́н	Гага́рин
Accusative	Юри	Валентин	Гагарин
Genitive	Юри	Валентин	Гагарин
Prepositional	Юри	Валентин	Гагарин
Dative	Юри	Валентин	Гагарин
Instrumental	Юри	Валентин	Гагарин

Here male name is composed of 2nd declension nouns, but there are exceptional endings for Instrumental. Female name is in 1st declension, but ending -ой is used for a family name in all oblique cases. Plural follows adjectival declension, except that Nominative is short -ы.