I. Convexity -- ยง1 Convex sets -- ยง2 Faces and supporting hyperplanes -- ยง3 Polarity -- ยง4 Direct sum decompositions -- ยง5 The lower semicontinuity of the operator โexpโ -- ยง6 Convex cones -- ยง7 The Farkas Lemma and its generalization -- ยง8 Separable systems of convex cones -- II. d-Convexity in normed spaces -- ยง9 The definition of d-convex sets -- ยง10 Support properties of d-convex sets -- ยง11 Properties of d-convex flats -- ยง12 The join of normed spaces -- ยง13 Separability of d-convex sets -- ยง14 The Helly dimension of a set family -- ยง15 d-Star-shaped sets -- III. H-convexity -- ยง16 The functional md for vector systems -- ยง17 The ?-displacement Theorem -- ยง18 Lower semicontinuity of the functional md -- ยง19 The definition of H-convex sets -- ยง20 Upper semicontinuity of the H-convex hull -- ยง21 Supporting cones of H-convex bodies -- ยง22 The Helly Theorem for H-convex sets -- ยง23 Some applications of H-convexity -- ยง24 Some remarks on connection between d-convexity and H-convexity -- IV. The Szรถkefalvi-Nagy Problem -- ยง25 The Theorem of Szรถkefalvi-Nagy and its generalization -- ยง26 Description of vector systems with md H = 2 that are not one-sided -- ยง27 The 2-systems without particular vectors -- ยง28 The 2-system with particular vectors -- ยง29 The compact, convex bodies with md M = 2 -- ยง30 Centrally symmetric bodies -- V. Borsukโs partition problem -- ยง31 Formulation of the problem and a survey of results -- ยง32 Bodies of constant width in Euclidean and normed spaces -- ยง33 Borsukโs problem in normed spaces -- VI. Homothetic covering and illumination -- ยง34 The main problem and a survey of results -- ยง35 The hypothesis of Gohberg-Markus-Hadwiger -- ยง36 The infinite values of the functional b, b2032;, c, c2032;, -- ยง37 Inner illumination of convex bodies -- ยง38 Estimates for the value of the functional p(K) -- VII. Combinatorial geometry of belt bodies -- ยง39 The integral respresentation of zonoids -- ยง40 Belt vectors of a compact, convex body -- ยง41 Definition of belt bodies -- ยง42 Solution of the illumination problem for belt bodies -- ยง43 Solution of the Szรถkefalvi-Nagy problem for belt bodies -- ยง44 Minimal fixing systems -- VIII. Some research problems -- Author Index -- List of Symbols

1. Mathematics
2. Geometry
3. Convex geometry
4. Discrete geometry
5. Calculus of variations
6. Combinatorics
7. Mathematics
8. Geometry
9. Convex and Discrete Geometry
10. Combinatorics
11. Calculus of Variations and Optimal Control; Optimization