This is the 1058th most frequent Russian word.
основных
"Основных" means "main" or "basic" in English.
In this context, "основных" (fundamental) is used as an adjective to describe "наук" (sciences), emphasizing their foundational nature.
Он изучил основы основных наук.
He studied the basics of the fundamental sciences.
Here, "основных" is used to describe "принципов" (principles), highlighting their essential or key importance.
Один из основных принципов этой теории — симметрия.
One of the fundamental principles of this theory is symmetry.
In this example, "основных" modifies "участников" (participants), indicating their primary or most important status.