It was their first album without covers and also the first record where they started to go beyond Blues and rock'n'roll stylistically; December's children has some moments like that but is actually not a real album but a record-company product that was not released in europe.

I know that "Out of our heads" are sometimes viewed as some breakthrough of sorts too but it's the same thing there:the album the Stones were behind themselves for the british market was largely R&B covers; the US-version replaced some of those songs with singles like Last time and Satisfaction and thus, it sounds a bit more like later Stones.

However, Aftermath was the *album* which Stones created themselves with the intention to make an original album that went beyond covers and music *purely* rooted in blues and rock'n'roll (songs like Lady Jane, Mother's little helper, Under my thumb and of course Paint it Black on the US version)...