The most striking feature of sintering is the complex evolution of particle and pore network shapes, which occurs to reduce total surface and grain boundary energies. This chapter explores the equilibrium structures that develop during the sintering of multiple particles to minimize total energy and derives geometric principles that define these equilibrium shapes. The naturally evolving surfaces and grain boundaries change their topology throughout the sintering process. The actual porous structure observed in sintering significantly differs from the classical idealized model. The interface topology clearly distinguishes the initial, intermediate, and final stages of sintering.