Throughout this chapter, we take many sophisticated ideas and break them down into simpler parts to explain the hidden structures of a singular foliation. We begin in Sect. 1 with the concept of “anchored bundles” in the context of a singular foliation, and proceed to present their morphisms and equivalences. This part concentrates exclusively on the \(\mathcal {C}^\infty (M)\) -module structure of the singular foliation \(\mathcal {F}\) . In Sect. 2, we go further by adding a bracket to an anchored bundle. This brings us to a concept known as the “almost Lie algebroid” associated to a singular foliation. This part now makes use of the Lie bracket. Subsequently, in Sect. 3, we discuss the notion of “isotropy Lie algebra and holonomy Lie algebroid” of Androulidakis-Skandalis. In Sect. 4, we discuss the concept of “bisubmersions”, also introduced by Androulidakis and Skandalis. These ideas help to explain how to define the “holonomy groupoid” of a singular foliation in Sect. 5.1. In Sect. 6, we discuss the notion of geometric resolution of a singular foliation (again, this uses only the structure of module over functions of a singular foliation), while Sect. 7 expends the notion of almost Lie algebroid over a singular foliation to something more general called the “universal Lie \(\infty \) -algebroid” (or “universal Q-manifold”) of a singular foliation.