This book provides a systematic description about the development of Isogeometric Topology Optimization (ITO) method using the density, and then addresses the effectiveness and efficiency of the ITO method on several design problems, including multi-material structures, stress-minimization structures, piezoelectric structures and also with the uniform manufacturability, ultra-lightweight architected materials with extreme bulk/shear moduli, auxetic metamaterials and auxetic meta-composites with the NPRs behavior in microstructures. A detailed MATLAB implementation of the ITO method with an in-house code “IgaTop” is also presented.