1 Borsuk's Problem. - 1 Introduction. - 2 The Perkal-Eggleston Theorem. - 3 Some Remarks. - 4 Larman's Problem. - 5 The Kahn-Kalai Phenomenon. - 2 Finite Packing Problems. - 1 Introduction. - 2 Supporting Functions Area Functions Minkowski Sums Mixed Volumes and Quermassintegrals. - 3 The Optimal Finite Packings Regarding Quermassintegrals. - 4 The L. Fejes Tóth-Betke-Henk-Wills Phenomenon. - 5 Some Historical Remarks. - 3 The Venkov-McMullen Theorem and Stein's Phenomenon. - 1 Introduction. - 2 Convex Bodies and Their Area Functions. - 3 The Venkov-McMullen Theorem. - 4 Stein's Phenomenon. - 5 Some Remarks. - 4 Local Packing Phenomena. - 1 Introduction. - 2 A Phenomenon Concerning Blocking Numbers and Kissing Numbers. - 3 A Basic Approximation Result. - 4 Minkowski's Criteria for Packing Lattices and the Densest Packing Lattices. - 5 A Phenomenon Concerning Kissing Numbers and Packing Densities. - 6 Remarks and Open Problems. - 5 Category Phenomena. - 1 Introduction. - 2 Gruber's Phenomenon. - 3 The Aleksandrov-Busemann-Feller Theorem. - 4 A Theorem of Zamfirescu. - 5 The Schneider-Zamfirescu Phenomenon. - 6 Some Remarks. - 6 The Busemann-Petty Problem. - 1 Introduction. - 2 Steiner Symmetrization. - 3 A Theorem of Busemann. - 4 The Larman-Rogers Phenomenon. - 5 Schneider's Phenomenon. - 6 Some Historical Remarks. - 7 Dvoretzky's Theorem. - 1 Introduction. - 2 Preliminaries. - 3 Technical Introduction. - 4 A Lemma of Dvoretzky and Rogers. - 5 An Estimate for ?V(AV). - 6 ?-nets and ?-spheres. - 7 A Proof of Dvoretzky's Theorem. - 8 An Upper Bound for M (n ?). - 9 Some Historical Remarks. - Inedx. Language: English