Ballot Theorems, Old and New -- Statistical Inference on Random Structures -- Proof Techniques for Factor Theorems -- Erd?s-Hajnal-type Results on Intersection Patterns of Geometric Objects -- Old and New Problems and Results in Ramsey Theory -- Forbidden Intersection Patterns in the Families of Subsets (Introducing a Method) -- Subsums of a Finite Sum and Extremal Sets of Vertices of the Hypercube -- Combinatorial Conditions for the Rigidity of Tensegrity Frameworks -- Polygonal Graphs -- Infinite Combinatorics: From Finite to Infinite -- The Random Walk Method for Intersecting Families -- Problems and Results on Colorings of Mixed Hypergraphs -- Random Discrete Matrices.