Differential geometry of singular spaces

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Korybut
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TL;DR Summary: Reference request

Hello!

Reading the book "Differential geometry of Singular Spaces and Reduction of symmetry" by J. Sniatycki https://www.cambridge.org/core/book...-of-symmetry/7D73498C35A5975594605428DA8F9267
I found that not every definition and statement is clear to me and alternative source of information is highly desirable. Can someone provide additional reference to this subject? Many thanks in advance