Besides writing marvelous sci-fi which I would recommend everyone to read, many of his books center around a world where humans rejuvenate. Basically you go to a clinic where your body's age is turned back to whatever age you desire (or maybe a new body is grown, can't remember). When you are there your "brain" (memories, thinking patterns etc) is backed up meaning if you are killed the clinic will simply clone a new body for you and download your consciousness to the new body. It's been I while since I last read his books so I can't off-hand remember what moral/social aspects of immortality he focused on.
If you want to read his books I would recommend you start with Pandora's Star and Judas Unchained. Those have to be some of the best books I've ever read. Speaking of which, I'm off to re-read them a third time.
His stories felt very much like the present, or the near past, projected into the future, with very little change.
This could be deliberate. The some of oldest people are also the richest (including having their own family planet), and least likely to want cultural change. The entire civilization could be bent to their desire to prevent change. But I don't think so. I think he just writes the present into the future.
Of course all authors find it hard to really think about a future culture different than their own. Take Heinlein, whose future worlds are often American pioneer or mid-20th century. But Heinlein added a few things to remind you that it is the future. Kilts are a trend in Methuselah's Children, white gloves for men in Double Star, nail polish for men in Beyond this Horizon, and at the end of Time For The Stars we realize that women throughout the story were always wearing hats, while back on Earth that fad had passed and women had naked heads "like an animal."
While in Pandora's Star and Judas Unchained, the future was now, with a few extra gadgets, and a view of sexism which already feels dated. (I agree with the comment about sexism at https://www.goodreads.com/review/show/149949969?book_show_ac... . And yes, Heinlein's stories were also sexist. I like the description that he write about a future with woman's lib, with women characters as doctors and engineers, but the reality of women's lib was quite different.)
On a technical side-note, the power sources really bug me. There are super-duper capacitors that can be charged over a century in order to change the weather, and incredible power sources that can be surgically embedded in humans so that a fight between two such augmented human ends up knocking down walls, but there are still diesel engines?
Also Pandora's Star and Judas Unchained are fantastic, towards the second half of JU I could not put it down - literally took a day off work to finish it.
If I may, I'd also like to suggest Richard K. Morgan for his Takeshi Kovacs trilogy, which is currently being turned into a TV series named after the first book, "Altered Carbon".
It is premised on backing up human consciousness to a "cortical stack" that can be recovered when a person is killed or dies, and downloading them into a new body, or "sleeve". It covers the rich overclass that effectively lives forever with a clone bank, criminal punishment being "put on ice" while someone else uses your body, and crack soldiers being deployed across planets digitally by being downloaded into new bodies. The whole series is a must read if you are contemplating the ethics and implications of immortality via digital backup.
That works across long distances, and even when different bodies travelling at different percentage of speed of light, thus experiencing different 'speed of time' (but that's marked as 'a rather unsettling experience' iirc).
Also, the group personality is affected by the individual tines.
The traeki in Brin's Uplift universe are a related example.
The Common Wealth and Void Sagas are great and sound to be what you are looking for.
Aging can be reversed, bodies can be clone and have a back you installed, genes can be modification. Death exist, but is almost always temporary.
Were he alive, Jules Verne would have been an excellent choice. Verne's tomb has a statue dedicated to immortality and eternal youth, https://en.wikipedia.org/wiki/Jules_Verne#/media/File:Verne_...
Diaspora (my favourite book) goes so far as to just stop counting time anymore because it just goes so unimaginably far.
"Dukaj has interesting take on post-humanism, both as a state of being and as a process. If you recall Accellerando, even though Manfred Macx was a futurist and trans-humanist he was hesitant to augment himself past certain limits. Stross pretty much drew a line in sand and said: up to here, you are human and if you rewire yourself further you will become something both incomprehensible, inhuman and frightening. Dukaj is very aware of this problem, but in his universe there is no line – there is a blurred spectrum of humanity. Yes, if you continue augmenting yourself for pure performance you may eventually lose track of your humanity." 
2. Hannu Rajaniemi
Wrote the Golden Ocumene trilogy which explores a post-post-singularity society where not only is immortality taken for granted, post-humans can swap between species and lifestyles, IRL or virtually, pretty much at will. Essentially the book itself explores the will to push boundaries in a world where everything conceivable is plentiful and readily available, and as a result, most of humanity and culture has grown stagnant, because how can you get better than perfect?
Perhaps he would be most famous for his short story "Overdrawn at the Memory Bank" which was dramatized on PBS. This production was later to be soundly mocked during the original run of Mystery Science Theater 3000.
I think he's not very well known, but his Triology fits the theme very well: It is about the engineer Bob, who is uploaded as a "replicant" into a spaceship. Humanity mostly wipes it self out using nukes after they got the Bob failsafe away into space, and Bob gets too deal with the remnants of humanity. He replicates himself, too the point that the Bobs can host a Bobmoot and vote on things. Due to being immortal, some Bobs starts calling humans ephemerals, wheras others are offended at the implication that they're not human.
It's a very interesting and entertaining read. I'm also writing this from the top of my head and have only read this triology by him.
Unfortunately it looks like the author, Natalie Babbitt, passed away last year. So they can't interview her.
Free download: https://coins.ha.com/information/tfi.s?type=-FIRSTIMMORTAL.C...
There's authors that achieve a sort of personnal connection with readers through their stories. Heinlein did that for me, along with the also greatly regretted Iain M. Banks.
His book The Uploaded deals with the consequences of a world where the dying are granted digital immortality in a fantasy filled utopian adventure, but they still get to vote. The real world is falling apart, few people care about their bodily existence, looking for any excuse to die, and the uploaded have all the political power.
Even our ancestors feared rule by the dead, which is where the rule against perpetuities comes from.
As soon as they have completed the term of eighty years, they are looked on as dead in law; their heirs immediately succeed to their estates; only a small pittance is reserved for their support; and the poor ones are maintained at the public charge. After that period, they are held incapable of any employment of trust or profit; they cannot purchase lands, or take leases; neither are they allowed to be witnesses in any cause, either civil or criminal, not even for the decision of meers (metes) and bounds.
It's a sad irony that an author who's work was so focused on immortality died at 58.
Hannu Rajaniemi - author of The Quantum Thief
What broadcasting company is this? VPRO?
Still worth reading.
They built a robot clone of him and his head made a run for it and is still on the lam.