Introducing Goodwillie calculus:
Tom Goodwillie, The differential calculus of homotopy functors, Proceedings of the International Congress of Mathematicians in Kyoto 1990, Vol. I, Math. Soc. Japan, 1991, pp. 621–6 (article pdf, full proceedings Vol I pdf, pdf)
Thomas Goodwillie, Calculus. I. The first derivative of pseudoisotopy theory, K-Theory 4 (1990), no. 1, 1-27 (doi:10.1007/BF00534191, MR:1076523)
Thomas Goodwillie, Calculus. II. Analytic functors, K-Theory 5 (1991/92), no. 4, 295-332 (doi:10.1007/BF00535644, MR:1162445)
Thomas Goodwillie, Calculus. III. Taylor series, Geom. Topol. 7 (2003), 645–711 (euclid:gt/1513883319 doi:10.2140/gt.2003.7.645, arXiv:math/0310481)
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