The following is from a blog on the development of group theory:
"Möbius in 1827, although he was completely unaware of the group concept, began to classify geometries using the fact that a particular geometry studies properties invariant under a particular group. Steiner in 1832 studied notions of synthetic geometry which were to eventually become part of the study of transformation groups."
My main interest is to delve into the development of Group Theory in regards to Geometry during the 19th century. What could I read in order to understand what Mobius and Steiner were studying at the moment and how they implicitly used the concept of a group to tackle particular problems?
I have studied Group Theory, however I have not studied Geometry, but I am willing to read any introductory text if necessary.
Thanks in advance.