The video tutorial by Katya explores the peculiarities of Russian grammar, focusing on the instrumental case. It explains the importance of cases in showing relationships between objects and provides examples of using the instrumental case with prepositions, tools, verbs, and fixed phrases. The tutorial covers how to use the instrumental case in different contexts, such as with the preposition 'with', certain verbs like 'to be', and in fixed phrases related to time of year and day.

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