This is a lovely little mindbender of a book - not hard science, for those who are so inclined. But a true literature of ideas, looking at identity and self through the lens of time travel, through one man (and all the versions of himself) and how he chooses to use it.
He is not a representative man, that's for sure. He is self-absorbed to a fault, choosing, once he has acquired a time travel belt, to socialize only with himself.
Which requires a digression into the kind of time travel Gerrold is hypothesizing. It is quite different from most of the SF in that vein that I'm familiar with. No paradoxes. No worries about interacting with other versions of the self, past or present. In fact, that's the way the narrator prefers it. No, instead of a whiteboard that is wiped clean with every change, he describes it as adding layers of paint to a wall - you can paint over as many times as you want, but the previous changes are till there. Eventually, the narrator comes to understand it as a proliferation of alternate universes, all of them inaccessible to himself once they have split, but real nonetheless. Where other Dons or Dans or Dannys - or, for that matter, Dianes or Donnas - have made other choices.
As a result, he changes the world freely, including major historical events. But that is not what the novel is about. These are throwaway lines, about how he occupies himself in a long life that is lived in a non-linear fashion. He talks about being unstuck from the seasons, from history, from weather. And yet, the feeling that comes across about this life of huge diversity and adventure are the ways in which his life is circumscribed. When he isn't travelling in time, his life is bounded by a single year to which he returns, and for the most part, to a central location - a mansion where he can always walk into a poker game with other versions of himself.
And his social circle is entirely bounded by himself, both for entertainment, and eventually, int arms of his sexuality. Although the character initially discovers his attraction to the past and future versions of himself, and acts upon them with more or less eagerness (the version who finally takes over the story revels in his discovery of his homosexuality), I would eventually come to dub his orientation "solipsexuality" - as he eventually starts a longer-term relationship with a female version of himself. But his sexuality is never turned any further outside than another version of himself. The narrator never sees this as a problem, but the walls he puts up around himself and his world, when he has all of time to play in, strike me as a bit tragic.
It's hard to say that there's a consistent narrator - in fact, it would be easy to argue that with each asterisk-break, another version picks up the story, with similarities to the previous but not identical to them. In one case, his sense of identity starts to break down into the psychotic, and has to be stopped by other versions of himself.
I'm sure I've served to confuse rather than enlighten you, but perhaps you'll take that as a reason to pick this up. It's a short little book, but the ideas within it are fascinating, but the character at the centre, perhaps, slightly sad. It is of a man who has become an island, even when surrounded by people, because they are all mirrors of himself.
I read this book as part of an attempt to read all the Hugo Nominees