This is the 2146th most frequent Russian word.
балета
The Russian word "балета" means "of ballet" (genitive case of "балет").
Here, 'балета' is in the genitive case, expressing that the production is of or related to ballet.
Премьер театра исполнил главную роль в постановке балета.
The theater's lead performer played the main role in the ballet production.
The word 'балета' is in the genitive case here as part of the noun phrase 'история русского балета,' specifying the type of history.
Она увлекается историей русского балета и часто посещает музеи.
She is enthusiastic about the history of Russian ballet and often visits museums.
In this case, 'балета' is also genitive, modifying 'школы,' and indicates the type of school.