A Short Course in Computational Geometry and Topology With the aim to bring the subject of Computational Geometry and Topology closer to the scientific audience this book is written in thirteen ready to teach sections organized in four parts: TESSELLATIONS COMPLEXES HOMOLOGY PERSISTENCE. To speak to the non specialist detailed formalisms are often avoided in favor of lively 2 and 3 dimensional illustrations. The book is warmly recommended to everybody who loves geometry and the fascinating world of shapes Roots of Geometry and Topology Voronoi and Delaunay Diagrams Weighted Diagrams Three Dimensions Alpha Complexes Holes Area Formulas Topological Spaces Homology Groups Complex Construction Filtrations PL Functions Matrix Reduction Epilogue