Information geometry relies on (differential) geometry to study (statistical) model families. We recommend basic knowledge in mathematical statistics, information theory, and differentiable manifolds. The following books are suggested:
I also wrote the following articles which may provide a smooth way to begin studying information geometry:

• Cramér-Rao Lower Bound and Information Geometry (arXiv:1301.3578), Connected at Infinity II: A Selection of Mathematics by Indians (2013): 18-37. chapter on publisher web site
• What is an information projection, Notices of the AMS, 65.3 (2018): 321-324.
• The many faces of information geometry, Notices of the AMS, 69.1 (2022): 36-45.
• An elementary introduction to information geometry, Entropy 22.10 (2020): 1100.
• Introduction to Information Geometry (40-minute tutorial)
• pyBregMan: A Python package for Bregman Manifolds

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