Complex sentence: The Rolling Stones were at the forefront of the British Invasion of bands that became popular in the US in 1964, and identified with the youthful and rebellious counterculture of the 1960s.
Split into simpler sentences: The Rolling Stones were at the forefront of the British Invasion of bands that became popular in the US in 1964. The band identified with the youthful and rebellious counterculture of the 1960s.