The Buddha refused to offer any teaching regards an Atman [or soul]. He did however make the teaching of 'anatta' the cornerstone of his philosophy.
The use of the word anatta in the Sutta Pitaka [the first of the 3 Pitakas which make up the Pali Canon, the source text for Buddhism] is always in reference to egocentric states of mind.
In Indian philosophy, there are 6 recognized systems of thought. They range from profoundly atheistic to thoroughly devotional.
The 'mystical' traditions, such as yoga, seek to grapple with the imponderables such as whether there is an eternal soul [or self] by attempting to first master the mind and transcend the ordinary human condition ... in the hope that this will then allow the practitioner to achieve a direct experience or insight into the actual nature of reality, by virtue of the fact their mind is unclouded. Leaving behind [transcending] one's vanity [ego] is a necessary part of that process.
The Buddha's aim appears to be a little different to that. His focus was on suffering and his teaching is concerned with avoiding that suffering which can be avoided. In his teaching 'dukkha' [usually translated as suffering but it has richer connotations than that] is a universal, i.e. it is part of the fabric of existence so can not be avoided.
However, there is that suffering which is self created and that can be avoided. Central to that is the suffering which is endured due to clinging to a fixed and fallacious 'self' [which when examined closely is found to be only a mental construct in the mind]. Gaining insight into one's own vain imaginings about oneself and abandoning them is key to avoiding the suffering which comes from 'clinging to those ideas.
It is a mistake to extrapolate, from that, the Buddha taught there was no soul or 'abiding self'. He steadfastly refused to offer any teaching about that one way or another. It was outside of his intentions and he treated it as a question which had no practical purpose while one was still immersed in 'suffering'.
