Computerized Tomography and discretization. The Radon transform and its inversion for X-ray image reconstruction. Applications and related problems. Discretization of the reconstruction process. The Matlab “radon” and “iradon” functions. Examples and applications. Reconstruction from a limited number of projections. The problem of ghosts. Models for discrete tomography. The reconstruction problem in the grid model as a linear system of equations. Investigation of the space of ghosts. Algebraic approach in a finite lattice grid and polynomial characterization of switching components. Discrete tomography. Uniqueness models. Uniqueness and additivity. A few notion of projective geometry. Cross-ratio and its invariance under projections and sections. The results of Gardner and Gritzmann in the integer lattice. A few remarks on polyominoes. Binary Tomography Bad configurations, weakly bad configurations, switching components, ghosts. Ryser algorithm and a few extensions. Examples of binary reconstruction and characterization of the set of solutions. A uniqueness theorem for binary tomography. Examples of reconstructions of differently shaped discrete binary objects in a finite grid, by exploiting suitable sets of four directions. Geometric Tomography Hammer’s problem and related uniqueness problems. Mid-point construction. U-polygons and their properties. The theorem of Gardner-McMullen in the Euclidean plane. Projections of convex bodies with point X-rays. The theorem of Volcic in the Euclidean plane. P-polygons. Some results and examples.