reference request – Which books should I read in order to be prepared to study Information Geometry?

At the moment, I am preparing my master’s thesis (in statistics) and I intend to keep studying in order to pursue a doctoral degree. To be precise, I am mainly interested in studying Information Geometry.

It is worth emphasizing that I have a bachelor’s degree in pure mathematics.

Having said that, I would like to be advised as to which books should I study in order to prepare myself to get acquainted to this subject.

More precisely, could someone tell me which books of differential geometry, probability and statistics should I read in order to introduce myself to it?

A progressive list of readings would be appreciated.