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This chapter reviews important notions and results on hyperplane arrangements required in the book. The discussion includes: 1) geometric objects such as faces, flats, bifaces, partial-flats, nested faces, lunes, bilunes, cones; 2) algebraic objects such as the Tits monoid, Birkhoff monoid, Janus monoid and their linearized algebras; Lie and Zie elements; 3) combinatorial objects such as distance functions and Varchenko matrices; descent, lune, Witt identities; incidence algebras, zeta and Möbius functions along with their noncommutative and two-sided analogues, the Zaslavsky formula and its noncommutative analogue.
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