Could it be Mike Resnick's [_Birthright: The Book of Man_](https://en.m.wikipedia.org/wiki/Birthright:_The_Book_of_Man)? It's the future history of mankind conquering the galaxy, losing control, and eventually dying out. It was published in 1982.

> Birthright spans a timeline of nearly 17 millennia, beginning at a very early stage of expansion from Earth and ending with the death of the last humans. In between, it chronicles a slow but (despite some set-backs) steady conquest of the entire galaxy - inhabited by thousands of sentient alien races, which are overpowered and oppressed using whatever tool it takes: economic pressure, diplomatic finesse, or simple military power.

> Not all chapters deal with humanity's treatment of aliens; some also cover the "internal" politics that result in a development of the growing human empire from a democracy to a monarchy. But the biggest theme is undeniably the search for the elusive quality that allows humanity to overcome all opposition and manage the unique feat of conquering the entire galaxy. It is never clearly defined but manifests perhaps most succinctly when it also results in the failure of an attempt to cross the void between galaxies.

[![Birthright: The Book of Man front cover][1]][1]

  [1]: https://i.sstatic.net/4a30o.jpg