The New Oxford Dictionary defines ‘self’ as:
A person’s essential being that distinguishes them from others,
A person’s particular nature or personality,
The qualities that make a person individual and unique.
Wikipedia defines ‘self’ as:
The self is the subject of one's own experience of phenomena, such as perception, emotions and thoughts.
The Buddha never defined (the) ‘self’ (Sanskrit: atma). He merely stated that (the) ‘self’ was not abiding, i.e. permanent (to wit, all emerged phenomena are anatta, i.e. without (abiding) self).
Victor’s definition of ‘self’:
A set of adaptation rules (that serves survival).
One’s adaptation state, to wit, ‘I am (i.e. my self is) how I have adapted’.