In this one, he seems like he's having a lot of fun nerding out about one of his favorite subjects.
There are a number of competing definitions of identity. Most people in the intended target audience, if they haven't thought it through already, default to a definition based on spiritual continuity: each person is a soul, which can change over time and be instantiated in different worlds but cannot stop existing. But that definition is unfalsifiable and not directly observable. If living people didn't have souls, and dead people were only copies of them, how would anyone ever know? These kinds of concerns give rise to other definitions. Maybe it makes sense to define identity based on observable facts about a person: if a newly dead person behaves just like they did when they were alive, remembers the same things they did when they were alive, and feels the same feelings they felt when they were alive, then maybe it doesn't matter if they were copied or teleported or something else. But they aren't identical; they see new things, and that makes them feel new things and do new things and make new memories. Over time they forget things. Over time they can change everything about themselves. An implication of defining identity based on specific traits is that this constitutes becoming a different person. But which parts constitute that? Does every change make someone a new person? Does having one thing in common with someone make you the same person? Most people reject both of those options. And he'll go into detail on some of the more popular specific definitions of identity, but first...
Why is this relevant to population ethics? In some cases it isn't; under, for example, total hedonic utilitarianism, it doesn't particularly matter if there are two people who are happy for a thousand years each, or one person who is happy for two thousand years. But under the person-affecting view, it's wrong to make someone less happy, but not wrong to cause a less happy person to come into existence instead of a happier one; it's therefore essential to define identity somehow. And under the maximin principle, the welfare of the worst-off person is the priority - so under certain interpretations, it matters which experiences belong to the same person. This is even a problem for all of ethics, not just population ethics - some definitions of personhood allow for one body and soul to have multiple persons simultaneously, making it hard if not impossible to distinguish between someone consenting to experience some pain for a later reward, and someone choosing to hurt someone else for personal gain - but this course is only about population ethics.
After the introduction, the rest of the course is organized around a few specific definitions of identity and personhood, going into detail about how each one would interact with each of a few specific ethical theories in a few example scenarios.