This chapter introduces the basic ways of speaking about sets, mappings, and relations. The order-theoretical concepts are discussed in detail. This includes an outline of the theory of cardinal and ordinal numbers and a proof of Zorn’s Lemma with its consequences such as the well-ordering theorem, comparability theorem for cardinal and ordinal numbers, and the product theorem for infinite cardinal numbers. Starting from the Peano axioms, an introduction to natural numbers is also provided. The basic tasks of elementary combinatorics are detailed. The Euclidean algorithm and the main theorem derived from it about the unique prime factor decomposition of natural numbers are the starting point of an introduction to elementary number theory and prepare the following chapter on the fundamentals of algebra.