Having established the functional analytic framework in Chapters 10, 11, and 12, here we take up the task of developing a comprehensive Calderón-Zygmund theory for singular integral operators on uniformly rectifiable sets in the context of firstgeneration Herz spaces, and other related scales. This is applicable to SIO’s of layer potential type associated with weakly elliptic systems, and provides the groundwork for employing boundary integral methods for the treatment of boundary value problems in Chapter 16. In Section 13.1 we focus on obtaining boundedness results for integral operators on first-generation Herz spaces Ap,. In Section 13.2 we treat singular integral operators on first-generation Herz-type Hardy spaces HAp,q.