The aim of this thesis is to introduce basic concept and results of geometric tomography according to parallel X-rays. We in- vestigate the di erence of the results concerning convex and non-convex sets. We also show that the vertices of a convex polygon with given coordinate X-rays form a lattice set in the plane. Then we investigate the spacial problem of counting the number of convex polygons with vertices chosen from a 3 3 planar lattice set. It turns out that this number can be 51, 56, or 61 depending on some conditions of the lattice set.