Contents -- Preface -- List of Figures -- List of Tables -- The Big Picture -- 1. Modern Physics at a Glance -- Geometry and Phase Transitions, in General -- 2. Phase Transitions and Critical Phenomena -- 2.1 Introduction -- 2.1.1 Evolution of the Universe: Decoupling of the Four Fundamental Forces -- 2.1.2 Three States of Water -- 2.1.3 Spins and Magnetism -- 2.2 Modern Classi.cation of Phase Transitions -- 2.3 First-Order Phase Transitions: Solid-Liquid Transition -- 2.4 Second-Order Phase Transitions: Scaling and Universality -- 2.5 RenormalizationGroup -- 2.5.1 Kadano. Picture: Coarse-Graining of Spin Blocks -- 2.5.2 General Formulation -- 2.5.3 Critical Exponents -- 2.5.4 Origin of Universality Class -- 2.5.5 Wilsonian Picture: Momentum-Space Renormalization Group -- 2.6 Mathematical Miscellanies: Semi-Group Structure and Fixed-Point Theorems -- 2.6.1 Semi-groups -- 2.6.2 Miscellany on Fixed-Points -- 2.7 Conclusion -- References -- 3. Overview of Density-Functional Theory -- 3.1 Introduction -- 3.2 Electronic Density-Functional Theory -- 3.3 ClassicalDensity-Functional Theory -- 3.4 Conclusion -- References -- 4. Survey of Solid Geometry and Topology -- 4.1 Introduction -- 4.2 Lattice Symmetry Groups -- 4.3 Two-Dimensional Space Groups -- 4.3.1 Hermann-Mauguin Crystallographic Notation -- 4.3.2 Orbifold notation -- 4.3.3 Why Are There Exactly 17 Wallpaper Groups? -- 4.3.4 Other Aspects of Topology in Physics -- 4.4 Three-Dimensional Point Groups -- 4.4.1 Face-centered Cubic (FCC) Lattices -- 4.4.2 Body-Centered Cubic (BCC) Lattices -- 4.4.3 A15 Lattices -- 4.5 Conceptual Framework of the Foam Model -- 4.6 The Kelvin Problem and the Kepler Conjecture -- 4.7 Conclusion -- References -- Geometry and Phase Transitions, in Colloidal Crystals -- 5. Lattice Free Energy via the Foam Model -- 5.1 Introduction -- 5.2 Bulk Free Energy.

5.3 Interfacial Free Energy -- 5.3.1 Charged Colloidal Crystals -- 5.3.2 Fuzzy Colloidal Crystals -- 5.4 Conclusion -- References -- 6. Phases of Charged Colloidal Crystals -- 6.1 Introduction -- 6.2 Phase Transitions of Charged Colloids -- 6.3 Foam Analogy and Charged Colloids -- 6.4 Conclusion -- References -- 7. Elasticity of Colloidal Crystals -- 7.1 Introduction -- 7.2 Foam Analogy and Cubic Elastic Constants -- 7.3 Elasticity of Charged Colloidal Crystals -- 7.4 Elasticity of Fuzzy Colloids -- 7.5 Conclusion -- References -- Geometry and Phase Transitions, in Topologically Constrained Polymers -- 8. Topologically-Constrained Polymers in Theta Solution -- 8.1 Introduction -- 8.2 O(N)-Symmetric φ6-Theory -- 8.3 Chern-Simons Theory and Writhe -- 8.4 One-Loop Scaling of Closed Polymers -- 8.5 Two-Loop Results -- 8.6 Conclusion -- References -- Summary -- 9. Final Thoughts -- Index.