Worth watching for those who know nothing about philosophy.
What is it that makes me me throughout my life? We might say the self, but what is the self? My body changes throughout my life. My interests, intelligence, pre-occupations and so on change throughout my life. So shouldn't my self too literally change throughout my life?
In order for the self not to literally change and avoid the conclusion I am literally a different person at time A than at time B, then the self has to be something distinct from all these things. I suggest the self is the author, or the experiencer, of one's thoughts, interests, and more generally of one's experiences. That is to say that in addition to experiences, there is an experiencer that has them. Experiences don't just exist without an experiencer, or self, to experience them. It is this author/experiencer/self that we can hypothesize remains unchanged.
Note that materialists can not believe in such an author/experiencer/self. This is because the materialist would have to identify any such self with some physical thing or processes. But physical things and processes are in a constant state of change, and certainly our bodies are. Hence, there is nothing unchanging which they can call a self.
They can of course believe in a sense of self. But the sense of a self differs from the actual self in a similar way to which a sense of a table differs from the actual table.
See the following blog entries by me:
Is a "life after death" conceivable? Part 3: What is the Self
Does the self as opposed to a mere "sense of self" exist?
The self and its experiences