This book develops a unified analytical framework for understanding the shape and stability of pendent drops governed by hydrostatic balance, pinned boundaries, and Rayleigh Taylor instability. Through a systematic treatment of both volume-controlled and pressure-controlled configurations, it shows how gravitational and capillary forces interact to produce turning points, symmetry-breaking transitions, and instability thresholds. By using potential-energy methods, variational principles, and symmetry arguments, the authors demonstrate that the full nonlinear behavior of drop configurations can be characterized without explicitly solving the associated eigenvalue problems. The resulting framework, based on a tractable one-dimensional model and extendable to axisymmetric and more general geometries, provides a clear approach for analyzing equilibrium drop behavior across a wide range of physical settings.