The catenary degree of the monoid of invertible ideals of non-maximal orders in quadraticnumber fields has been studied before and some upper bounds have been known for someyears, but the precise value remained unknown. The main result of this thesis (Theorems12 and 13) is the determination of the catenary degree of the monoid of invertible idealsfor all orders in quadratic number fields. Along the way, the set of distances of thismonoid is determined for all but a very special class of orders.The method employed makes use of a very detailed knowledge of the irreducible, in-vertible, primary ideals involved. Not only their structure, but also their distributionin terms of the ideal norm is known. This knowledge is spread among several researchpapers and several decades. The associated results are collected, reformulated and re-proved.