This is the 15260th most frequent Russian word.
посвященную
"Dedicated" or "devoted."
Here, "посвященную" is an adjective modifying "фильм," showing that the film is about or devoted to the life of the artist.
Мы смотрели фильм, посвященную жизни известного художника.
We watched a film dedicated to the life of a famous artist.
In this case, "посвященную" describes the exhibition, implying that its theme or focus is contemporary art.
Они организовали выставку, посвященную современному искусству.
They organized an exhibition dedicated to contemporary art.
In this sentence, "посвященную" functions as an adjective describing the book, indicating that its content is focused on or dedicated to the history of Russia.