Self-assembly is one of the most important concepts of the 21st century. Strikingly, despite the rational design of molecules for biological and pharmaceutical applications is rather well established, only few are the attempts to formally refine predictions of self-assembly in material science. In the present tutorial review, we encompass some of the most significant efforts towards the systematic study of (thermodynamically stable) self-assembly. We discuss experimental and computer-simulated self-assembly events in hard-matter, soft-matter and higher symmetry architectures under the common framework of partition functions. In this framework, we endeavor to correlate state-of-the-art chemical design, programming and/or engineering of reversible (thermal and chemical equilibrium) self-assembly with knowledge of the underlying partition function landscape in a step towards quantitative predictions and ab initio molecular design.