The fundamental point: what kind of immortality are we talking about? Does everyone look young or decrepit?
It is quite obvious that such a radical change, contrary to the biological vector that guides a person, will cause unprecedented changes in society.
First, the value of life will increase many times over, that will affect the willingness to take risks (army, police, crime, extreme sports). Attitudes towards bad habits (drinking, smoking) and transport (risk) will change.
Secondly, all social behavior (love, career) will change dramatically. If youth will last hundreds of years, then you can start looking for an "ideal" partner or your professional mission.
It is not entirely clear how viruses, bacteria and other microorganisms will behave. :)
Another interesting question is reproductive function. In women, they now end at about 45 years, in men much later, but not from the standpoint of immortality.
And if you remember about religion ...
to a terrible overpopulation There are several novels on this topic, the most recent, it seems, is the novel "The Future" by Dmitry Glukhovsky The action takes place in the 25th century, 300 years after the invention of the vaccine of immortality, which stops the aging process. As a result, a new way of life, a new morality, morality, a new attitude to life appears The population is strictly regulated, the birth of a child is actually outlawed Read, an interesting thing. The novel seems to be written in 2013