I am inclined to believe that the history of Buddhism is more than often a history of misconceptions, one piled upon the other forming an impressive edifice but one, nevertheless, unsound.
One important misconception that keeps popping up is that the Buddha denied a soul which in Sanskrit is ātman. And because he denied an ātman there cannot truly be any such thing as transmigration from one life to the next (another misconception).
Nevertheless, it is ever so clear, if one reads the Nikayas of the Pali canon, that the Buddha asks his monks not to regard as the ātman (in Pali attā) that which is not the ātman (S., an-ātman) this being the conditioned five aggregates or the psychophysical man. If the monk fails to do this, instead, regarding as the ātman the five aggregates, then clinging to this false ātman will bring about entanglement in samsara (the repeated cycle of birth and death).
As for the misconception that without the ātman there is logically no rebirth since the ātman is what transmigrates from one life to the next, this view is patently false. The Buddha has only said that it is consciousness (S., vijñāna) which fares on from one life to the next. At the same time, consciousness does not fare on without change of identity. In the case of Sāti who believed, otherwise, that consciousness fares on without change of identity (tadeva ... anaññam), this amounts to heresy since consciousness only fares on with change, the changing being karmic impressions or saṁskāra.
Ātman is at the core of Buddhism, but the idea that it is to be known by positing various views or hypotheses about it is frankly absurd. It can only be known by abandoning desire for whatever is not the ātman. This is an awakening process and also mystical negation which makes up dhyana or meditation. Naturally, what cannot be abandoned is the ātman. Only the anātman can be abandoned which is conditioned. And here lies the means to the ātman which in Mahayana Mahaparinirvana Sutra will be equated with the Buddha-nature.