I am seeking recommendations for books or resources that provide an engaging introduction to integral geometry, with a particular interest in Crofton's formula and its various proofs. I am looking for both classical texts that lay the foundational aspects and modern works that delve into applications across different fields. A balance between theoretical depth and practical insights would be ideal. Any suggestions that cover the historical evolution of these concepts alongside contemporary developments would also be highly appreciated.
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1$\begingroup$ The standard classical source is Santaló. $\endgroup$– Ted ShifrinCommented Mar 22 at 14:19
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$\begingroup$ Another beautiful book on this is the one by Klain and Rota. faculty.uml.edu//dklain/blurb.html $\endgroup$– DeaneCommented Mar 22 at 20:26
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