1. Convex sets in vector spaces.- 2. Brunn-Minkowski inequality.- 3. Convex polyhedra.- 4. Two classical isoperimetric problems.- 5. Some infinite-dimensional vector spaces.- 6. Probability measures and random elements.- 7. Convergence of random elements.- 8. The structure of supports of Borel measures.- 9. Quasi-invariant probability measures.- 10. Anderson inequality and unimodal distributions.- 11. Oscillation phenomena and extensions of measures.- 12. Comparison principles for Gaussian processes.- 13. Integration of vector-valued functions and optimal estimation of stochastic processes.- Appendix 1: Some properties of convex curves.- Appendix 2: Convex sets and number theory.- Appendix 3: Measurability of cardinals.