This book addresses the physical mechanisms involved in the characteristic electrical properties and the geometrical structures that are observed from dipolar monolayers composed of organic molecules by using dielectric physics, electrostatics, the physics of liquid crystal, and soft matter physics. The orientational order parameters, introduced to quantify the orientational structures of monolayers, guide us towards this goal. Dielectric polarizations are spontaneously generated from monolayers because of their orientational structures, and electrostatic energies due to these dielectric polarizations play a key role in forming the geometrical structures that are observed from monolayers. Free energy minimization is a powerful tool to understand the physical mechanisms that stabilize these geometrical structures because of the soft matter nature of monolayers. The approach using mathematical differential geometry method makes this book unique among the literatures of monolayers. Sample Chapter(s) Preface Chapter 1: Introduction Contents: Introduction Dielectric Physics of Monolayers; Theory of Dielectric Polarization of Monolayers Dielectric Physics of Monolayers: Experimental Techniques to Measure Dielectric Polarizations of Monolayers Liquid Crystalline Properties of Monolayers on Water Surface Differential Geometry Method for Analyzing Domain Shapes Differential Geometry Method for Analyzing Domain Shapes II Comprehensive Approach for Analyzing Domain Shapes Readership: This book would be useful for physicists, chemists, biologists and electronic engineers of the field to understand their experimental results and to develop new theories.