For traditional Buddhists, the experience of "self" or atta is considered an illusion, like a mirage, or perhaps a rainbow. The argument is that the phenomenological world is impermanent and formless, so the things that we experience via the senses are not representative of the "real stuff" out there. The self is built on these, so itself is also impermanent, and not an eternal quality. It's not bad exactly - later traditions posit that these aggregates or skandas of the self are the root of personality - but clinging to the impermanent self or samsaric phenomenon is, well, the root of suffering. And Buddha's all about suffering; if hypocrisy was Christ's kryptonite, then suffering is definitely the Shakya Buddha's. There's also another word for "self" that identifies with a sort of universal self, which is actually eternal, but it's also completely incomprehensible, by definition of its being infinite. And there's a whole bunch of later traditions. It's a lot to unpack.
I'd recommend picking up a good survey, some I remember as an undergrad were :
The First Cities, D. Hamblin
The Wonder that was India, A. Bassam
Indian Atheism, D. Chattopadhyaya, who also did a survey on Lokayata, an early Materialist movement in the subcontinent.
I'd recommend picking up a good survey, some I remember as an undergrad were :
The First Cities, D. Hamblin
The Wonder that was India, A. Bassam
Indian Atheism, D. Chattopadhyaya, who also did a survey on Lokayata, an early Materialist movement in the subcontinent.