The Prepositional Case
In the hallway, Anna gave Igor's book to Ivan. В коридоре, Анна дала Ивану книгу Игоря.
"In the hallway" ("в коридоре") is a prepositional phrase (also named after the Latin grammar term "locative" to describe position or location -- a frequent use of the prepositional case in Russian). The prepositional case requires a preposition, though not all prepositions require the prepositional case (most, actually, require other cases). Usually, the prepositional case is used to describe location in two instances, and is used to express "about" as in to talk about something.
There are three prepositions which can require the prepositional case:
"В" ("v") meaning "in" ("in the hallway"/"в коридоре")
"НА" ("na") meaning "on" or "at" ("on the table"/"на столе")
"О" ("o") meaning "about" (this is not location!) ("about the student"/"о студенте").
These three prepositions are among the few that use this case -- a case which is often taught first in Russian classes, even before the nominative!
Below is a chart of the prepositional case endings, with nouns listed first, and adjectives second in each gender. Please note that the nominatives are listed in the middle, and the prepositionals are on the right. Remember, too, that each ending can vary according to set rules depending on the hardness or softness of the stems, and on the spelling rules.
masculine and neuter endings are the same for both nouns and
**This ending is for feminine nouns ending in "-а, -я" only, and is the same ending as those of the DATIVE case for feminine adjectives and nouns. However, for feminine nouns ending in "-ь", such as "новость" ("news") the ending is "-и" (which is the same ending that these nouns use for the nominative plural, and all case endings -- including the prepositional -- in the singular except for the INSTRUMENTAL case). The adjective, of course, remains the standard feminine dative case adjective.
Test yourself with the prepositional case exercises.