The main aim of this chapter is to study Herz spaces of first generation Ap, in the setting of unbounded Ahlfors regular sets. We establish a wealth of fundamental properties for this scale of spaces, such as embeddings, natural versions of Lebesgue’s Monotone Convergence Theorem and Lebesgue’s Dominated Convergence Theorem, completeness, density, duality results, and boundedness of the Hardy-Littlewood maximal operator. Significantly, we find that Herz spaces of first generation fall within the scope of Generalized Banach Function Spaces (in the sense of [GHA-II]).