This could be summed up quite nicely as "The Last Six Lives of Milo". That reference is intentional, as there are a lot of similarities between the two books, and all for the good.
Milo is part of the eternal cycle of life, death and rebirth, going through his many lives until he can find Perfection and move on to the Oversoul (call it Nirvana, or similar as you like).
Finding Perfection is a tricky task, requiring some form of great personal sacrifice for the betterment of mankind. Buddha got his Perfection, mostly by being the Buddha. Milo can't find his.
You get ten thousand goes at finding perfection. That sounds like a lot. It is a lot. Milo is rubbish at it. He's been a space explorer, a village leader, one of the Buddha's fans, a simple fisherman (not that one) and a dog. Couldn't get Perfection in any of them. Not even that time he caught his own tail.
The book gives you short bits of many of his lives, which of course are all part of the same timeline, so occasionally overlap, or have effects on things in future lives. Presumably at some point, he might have met himself.
Nobody's ever really sure why he's so bad at this, because after nine thousand, nine hundred and four lives, of which he can remember a fair bit, he's pretty damn wise. Perhaps it's because he loves Death.
Every time he ends a life (by dying, not in the form of some millennia-spanning murderer (though now I kinda want to read that book)), he is met by Death, a part of the basic fabric of the universe, taking the form of Suzie. He rather fancies her. (I'm assuming she takes the form of the Gaiman Death.)
She has problems of her own, as being an immortal force of nature can occasionally get a bit boring. She wants to open a candle shop.
It's a fun, clever book. There's some interesting SF sneaked in here when we see his future lives, and in general, there's something interesting in each of them. And good lord is he a likable character.