Discontinuous (First-Order) Phase Transitions Constitute The Most Fundamental And Widespread Type Of Structural Transitions Existing In Nature, Forming A Large Majority Of The Transitions Found In Elemental Crystals, Alloys, Inorganic Compounds, Minerals And Complex Fluids. Nevertheless, Only A Small Part Of Them, Namely, Weekly Discontinuous Transformations, Were Considered By Phenomenological Theories, Leaving Aside The Most Interesting From A Theoretical Point Of View And The Most Important For Application Cases. Discontinuous Phase Transitions In Condensed Matter Introduces A Density-Wave Approach To Phase Transitions Which Results In A Unified, Symmetry-Based, Model-Free Theory Of The Weak Crystallization Of Molecular Mixtures To Liquid-Crystalline Mesophases, Strongly Discontinuous Crystallization From Molten Metals And Alloys To Conventional, Fully Segregated Crystals, To Aperiodic, Quasi-Crystalline Structures. Assembly Of Aperiodic Closed Virus Capsids With Non-Crystallographic Symmetry Also Falls Into The Domain Of Applicability Of The Density-Wave Approach. The Book Also Considers The Applicability Domains Of The Symmetry-Based Approach In Physics Of Low-Dimensional Systems. It Includes Comparisons Of Stability Of Different Surface Superstructures And Metal Monoatomic Coverage Structures On The Surface Of Single-Crystalline Substrates. The Example Of The Twisted Graphene Bilayer Demonstrates How Parametrization In The Spirit Of An Advanced Phenomenological Approach Can Establish Symmetry-Controlled, And Therefore Model-Free, Links Between Geometrical Parameters Of The Twisted Bilayer Structure And Reconstruction Of Its Brillouin Zone And Energy Bands.
