ABSTRACT
By the Fundamental Theorem of Arithmetic, every positive integer is a product of primes in an essentially unique way. In more general structures (monoids or integral domains) such a factorization into irreducible elements may exist, but needs by no means to be unique. The main objective of factorization theory is a systematic treatment of phenomena related to the non-uniqueness of factorizations in monoids and integral domains. In this chapter, we introduce the basic notions of factorization theory and give several examples which can be understood without a deeper understanding of the theory.
