This is the 782nd most frequent Russian word.
государственного
"State" or "of the state."
In this sentence, the word 'государственном' is an adjective modifying 'университете' and describes its public/state nature.
Он работает в государственном университете.
He works in a state university.
Here, 'государственного' is used in the genitive case to describe 'управления', indicating its relation to the state.
Принципы государственного управления изменились за последние годы.
The principles of state governance have changed over the last years.
In this sentence, 'государственного' serves as an attributive adjective for 'бюджета', referring to its national or public character.