Overview and preliminaries. Computer-assisted Theorem Proving in Synthetic Geometry. Coordinate-Free Theorem Proving in Incidence Geometry. Special positions of frameworks and the Grassmann-Cayley Algebra. From Molecular Distance Geometry to Conformal Geometric Algebra. Tree-decomposable and Underconstrained Geometric Constraint Problems. Geometric Constraint Decomposition: The General Case. Dimensional and Universal Rigidities of Bar Frameworks. Computations of metric/cut polyhedra and their relatives. Cayley Configuration Spaces. Constraint Varieties in Mechanism Science. Real Algebraic Geometry for Geometric Constraints. Polyhedra in 3-Space. Tensegrity. Geometric Conditions of Rigidity in Nongeneric settings. Generic Global Rigidity in General Dimension. Change of Metrics in Rigidity Theory. Planar Rigidity. Inductive constructions for combinatorial local and global rigidity. Rigidity of Body-bar-hinge Frameworks. Global rigidity of two-dimensional frameworks. Point-line frameworks. Generic rigidity of body-and-cad frameworks. Rigidity with polyhedral norms. Combinatorial rigidity of symmetric and periodic frameworks.