Sets, Functions, and Relations. Sets, valuations, and Boolean algebras
Functions, partitions, and entropy
Matching Theory. What is matching theory?
Free and incidence matrices
Submodular functions and independent matchings
Rado's theorem on subrelations
Doubly stochastic matrices
Matching theory in higher dimensions
Partially Ordered Sets and Lattices. Möbius functions
Modular and linear lattices
Finite modular and geometric lattices
Valuation rings and Möbius algebras
Generating Functions and the Umbral Calculus. Generating functions
Elementary umbral calculus
Polynomial sequences of binomial type
Umbral composition and connection matrices
The Riemann zeta function
Symmetric Functions and Baxter Algebras. Symmetric functions
Distribution, occupancy, and the partition lattice
Enumeration under a group action
Identities in Baxter algebras
Symmetric functions over finite fields
Historical remarks and further reading
Determinants, Matrices, and Polynomials. Polynomials
Totally positive matrices
Exterior algebras and compound matrices
Eigenvalues of totally positive matrices
Variation decreasing matrices
Pólya frequency sequences
