The prepositional case is the sixth and final case in Russian, though due to its relative simplicity it is often learned before the more complex genitive, dative, and instrumental cases.
Words decline into a case for two broad reasons: because they match that case's primary function (the nominative denotes the verbal subject, the accusative denotes the verbal object, etc), or because they come after a preposition that commands that particular case (у calls the genitive, между calls the instrumental, etc). The prepositional case is so called because it is only ever used after prepositions. Historically, the prepositional case was called the locative case as it did have a main function, which was to denote the location of something. This use has been taken over by prepositions, so it's name was changed accordingly. However, you may still hear it referred to by it's old name, and some words still bear hallmarks of the old locative case.
The four prepositions that call this case are о/об/обо ('about'), при ('on') в ('in'), and на ('on'). Notice that these last two are locative in meaning when they call the prepositional case.
- О/об/обо means 'about', and denotes the person or thing about which some verb is done ('they were talking about him', они говорили о нём).
- When the following word begins with a vowel, о becomes об ('I heard about the bus', я послышал об автобусе).
- Before awkward clusters of consonants, it becomes обо ('Boris read about me', Борис читал обо мне).
- При means 'on' or 'on one's person' ('She has an umbrella on her', У её есть зонтик при себе), and 'during' ('This happened during the reign of Peter I', Всё это случилось при Петре первом). As you might guess, this preposition is quite rare
- В means 'in' or 'at', referring to the the location of a person or thing ('I'm in Moscow', я в Москве).
- На means 'on' or 'at', and like в refers to the location of something ('He's on the roof', Он на крыше).
At a place 
The word 'at' is translated using в + prep', на + prep', and у + gen.
If you wished to say someone or something is at an enclosed building, such as 'He is at the theatre', use в + prep, as he is in that particular place: Он в театре. To say someone or something is at a particular street, such as 'She lives at Tverskaya street', use на + prep, as she is on something, rather than in it: Она живёт на Тверской улице. In general, if the place where someone or something is 'at' is an inanimate structure that humans normally go inside, use в + prep (e.g., 'They were at the theatre', 'He was at Moscow for the meeting'), otherwise use на + prep (e.g., 'They were at the field'). If the place is animate, instead use у + gen, meaning 'by someone's place' (e.g., 'They were at Sasha's')
В and на can also call the accusative case to refer to the direction towards which something is moving into or onto ('I'm walking into Moscow', 'He climbed onto the roof'). As a memory aid, recall that when в and на refer to the location of something, they use the prepositional case, which was once called the locative case. О/об/обо calls the accusative to mean 'against' or 'upon' something ('He leant upon the wall').
- Let's talk about the weather - Дава́йте говори́ть о пого́де
- They'll read about Aeroflot tomorrow - Они́ прочита́ют об Аэрофло́те за́втра
- She told a story about me - Она́ рассказа́ла расска́з обо́ мне
- Boris lives in Liverpool - Бо́рис живёт в Ливерпул́е
- Tatya is at work - Та́тя в рабо́те
Forming the prepositional case is arguably easier than any other case.
To form the prepositional case, in general, you add е (pronounced yeh):
- Masculine and neuter nouns ending in a consonant add e, and nouns ending in й, o, or ь, replace that letter with е. Nouns ending in ий instead become ии.
- About the garden - Сад --> Саде
- About the train - Поезд --> Поезде
- About the museum - Музей --> Музее
- About the letter - Письмо - Письме
- Feminine nouns ending in а or я replace that letter with е. Those ending in ь instead replace that letter with и. Feminine nouns that end in ия become ии.
- About the book - Книга --> Книге
- About the bird - Птица --> Птице
- About the pig - Свинья --> Свинье
- About mother - Мать --> Матери - note the addition of -ер- when мать declines
- Neuter nouns ending in е are unchanged, unless they end in ие, in which case they become ии. Those that have the exceptional ending мя become ени (though this is fortunately quite rare).
- As you might have guessed from the above, always write ии instead of ие
- Some nouns have a stressed у or ю after в + prep and на + prep, but not after о/об/обо + prep. This is the final hallmark of the old locative meaning of this case, as it can be seen as an ending that only occurs after locative prepositions ('in' and 'on'). See here for a list of such words.
In general, add or replace with е, but always have ии instead of ие.
The two plural endings, ах and ях, follow the same rules as the instrumental and dative plurals: after consonants, o, or а, use the ending ах. If such a noun has an irregular nominative plural ending in я (e.g., друг --> друзья), or if the noun ends in ь, й, е, or я, the ending is ях (e.g., друг --> друзья --> друзьях).
- About the gardens - Сад --> Садах
- About the trains - Поезд --> Поездах
- About the museums - Музей --> Музеях
- About the letters - Письмо - Письмах
- About the books - Книга --> Книгах
- About the birds - Птица --> Птицах
- About the pigs - Свинья --> Свиньях
- About the mothers - Мать --> Матерях
One exception is feminine nouns ending in мя, which instead take the ending енах. Again, this ending is fortunately quite rare.
(ий --> ии)
(ие --> ии)
(мя --> ени)
|а, я --> е
ь --> и
(ия --> ии)
(мя --> енах)
Rules in italics are rare exceptions to the more general rules.
Adjectives modifying masculine or neuter nouns in the prepositional case usually end in ом. For adjectives with the soft ending (ний), or for those whose stem ends in the 5-letter rule (ш, щ, ч, ж, ц), the ending is ем.
Like nouns, adjectives in the prepositional plural end in "х", and in fact take the same endings as the genitive plural: ых or, for those which normally end in ий, их.
|Adjectives||ом ем||ой ей||ых их|
- I heard about your beautiful new wife - Я слышал о красивой новой жене
- They're talking about those old Russian cars in the big red garage - Они говорят об этих старых русских машинах в большом красном гараже
The possessive pronouns in the prepositional case are as follows:
The third person singular personal pronoun нём is masculine and neuter, and ней is feminine.
The possessive pronouns are as follows:
|Your (sg., informal)||Твоём||Твое́й||Твои́х|
|Your (pl., formal)||Ва́шем||Ва́шей||Ва́ших|
As ever, possessive pronouns conjugate almost exactly like adjectives. The possessive pronouns in the third person are его for masculine and neuter owners ('his' and 'its), её for feminine owners ('her'), and их for plural owners ('their'). These are the same in all cases.
- I am reading about them - Я чита́ю о них
- I am reading about their children - Я чита́ю о их де́тях
This and that 
Remember that о ('about') becomes об before the vowel э.
- Exhaustive explanation of Russian prepositions: 
- List of nouns that decline irregularly in the prepositional case: 
|Russian language · Русский язык|
|Lessons||Introduction · Alphabet · Lesson 1 · Lesson 2 · Lesson 3 · Lesson 4 · Lesson 5|
|Reference||Numbers · Cases (Nom. · Gen. · Dat. · Acc. · Inst. · Prep.) · Adjectives · Prepositions · Verbs (Aspect · Past · Future) · Pronouns (Personal · Possessive · Interrogative) · Cursive|
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