Introduction -- Discrete Spaces: Graphs, Lattices, and Digital Spaces -- Euclidean Space and Continuous Space -- Digital Planar Geometry: Curves and Connected Regions -- Surfaces and Manifolds in Digital Space -- Algorithms for Digital Surfaces and Manifolds -- Discrete Manifolds: the Graph-Based Theory -- Discretization, Digitization, and Embedding -- Combinatorial Topology and Digital Topology -- Geometric Measurements and Geometric Computing -- Digital Functions, Data Reconstruction, and Numerical Geometry -- Geometric Search and Geometric Processing -- Discrete Methods in Differential Geometry -- Advanced Digital Topology and Applications -- Select Topics and Future Challenges in Discrete Geometry.