Anicca (impermanence) and anatta (nonself) are two "marks of existence" at the base of the Buddhist teaching and they're common to all schools. Nonself is related to impermamence and to "dependent co-arising". Impermanence means that nothing is fixed and unchanging, while dependent co-arising means that everything manifests and unmanifests according to the presence or abscence of conditions and there is nothing that exists "by itself".
Then with the Yogachara school of Mahayana there was a "mapping" of the human consciousness, which is described as composed by 8 consciousnesses. The last two are not present in Theravada texts. There are the six sense conciousnesses (the five senses + the "mind" sense, the one that perceives thoughts); the 7h consciousness, manas (the one that gives rise to the sense of self by grasping at the eight consciousness; this one is the closest to our "ego") and the 8th consciousness, alayavijnana ("storehouse consciousness"), that bears karmic seeds resulting from the impressions of other consciousnesses and from previous lives, in fact this is the only consciousness that survives between lives.
When alayavijnana is purified/transformed and freed from the grasping of manas, there is awakening / liberation. It becomes the "Great Mirror Wisdom" consciousness because reality is perceived as it is, free from defilements. In Chan/Zen Buddhism the Great Mirror Wisdom consciousness is identified with the Buddha-Nature that is present in all beings. This concept is also akin to the "Luminous Mind" of Buddhist Tantra.
Some people see this as a comeback of the self in a different form, but the counterargument to this is that Great Mirror Wisom and Buddha-Nature are just words to describe what is beyond concepts, so it is not a comeback of the self. Some texts use "negative" descriptions of nonself, especially in a culture where almost everyone believed in the existence of a soul, to avoid eternalism. Some texts use "positive" descriptions of nonself to avoid nihilism.
All the teachings are provisional.