Nil Bohr-sets and almost automorphy of higher order

* Introduction* Preliminaries* Nilsystems* Generalized polynomials* Nil Bohr$_0$-sets and generalized polynomials: Proof of Theorem B* Generalized polynomials and recurrence sets: Proof of Theorem C* Recurrence sets and regionally proximal relation of order $d$ $d$-step almost automorpy and recurrence sets* Appendix A* Bibliography* Index