Combinatorics in Banach Space Theory (University of Warsaw 2014/15)
Here you may download the lecture notes in Polish (which are still to be updated/corrected):

Notes (uploaded on 18.01.2015)
Analiza matematyczna II.1 (Uniwersytet Warszawski 2014/15)
Combinatorics in Banach Space Theory (University of Silesia 2012/13)

Combinatorics in Banach Space Theory 1. Almost disjoint families and Rosenthal's lemma with their applications: Phillips' lemma, Schur's property of \(\ell_1\), the structure of weakly compact operators on injective Banach spaces, noninjectivity of \(\ell_\infty/c_0\). Basic properties of weakly compactly generated (\(\mathsf{WCG}\)) Banach spaces. The JohnsonLindenstrauss space as an example showing that being \(\mathsf{WCG}\) is not a threespace property. A quantitative version of Krein's theorem on weak compactness of the closed convex hull of a weakly compact set, via Pták's combinatorial lemma. Steinitz's lemma and Lyapunov's theorem on the range of a vector measure; \(B\)convex spaces; KaltonGiesy theorem: \(B\)convexity is a threespace property. Rudiments of the threespace problem; \(K\)spaces; KaltonRoberts theorem on nearly additive set functions; \(c_0\) and \(\ell_\infty\) are \(K\)spaces.

Combinatorics in Banach Space Theory 2. Basics of Ramsey theory: the Ellentuck topology, completely Ramsey sets, the GalvinPrikry theorem, and their applications in the proof of Rosenthal's \(\ell_1\)theorem. Elements of the theory of bases and basic sequences in Banach spaces; the BessagaPełczyński selection principle. The ErdösMagidor dichotomy and its consequence: the closedness of the BanachSaks operator ideal. Construction of the Tsirelson space, i.e. a separable reflexive Banach space with no copy of \(\ell_p\) (\(1\leq p<\infty\)) and \(c_0\). Enflo's construction of a separable reflexive Banach space failing the approximation property (and thus not having a Schauder basis). The (sketch of the) GowersMaurey solution of the unconditional basic sequence problem.
Here you may download the lecture notes and some accompanying files.