I. M. James, History of Topology.

This is a collection of 40 essays by different authors, on topics related mostly to manifolds and algebraic topology.

Perhaps the page

http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Topology_in_mathematics.html

will be of interest for aspects of topology before Poincaré came on the scene.

I. M. James, History of Topology.

This is a collection of 40 essays by different authors, on topics related mostly to manifolds and algebraic topology.

Perhaps the page

https://mathshistory.st-andrews.ac.uk/HistTopics/Topology_in_mathematics/

from the MacTutor History of Mathematics site will be of interest for aspects of topology before Poincaré came on the scene. Their general topics history page is https://mathshistory.st-andrews.ac.uk/HistTopics/.