Introducing polyfolds for symplectic topology:
Helmut Hofer, A general Fredholm theory and applications (arXiv:math/0509366)
Helmut Hofer, Kris Wysocki, Eduard Zehnder,
A general Fredholm theory I: A splicing-based differential geometry (arXiv/0612604)
A general Fredholm theory II: implicit function theorems (arXiv:0705.1310)
A general Fredholm theory III: Fredholm functors and polyfolds (arXiv:0810.0736)
Helmut Hofer, Kris Wysocki, Eduard Zehnder, Integration theory for zero sets of polyfold Fredholm sections (arXiv/0711.0781)
Helmut Hofer, Polyfolds and a general Fredholm theory (arXiv/0809.3753)
Helmut Hofer, Polyfolds and Fredholm Theory, Oxford University Press (2017) (doi:10.1093/oso/9780198784913.003.0004)
Lecture notes:
Introducing Hofer's metric on Hamiltonian diffeomorphisms:
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