All possible torsion groups of elliptic curves \(E\) defined over a quadratic field \({\mathbb Q}({\sqrt{d}})\) are known and a parametrization of the curves having such groups has been given by Rabarison. In the paper under review, the authors construct for each of these groups a curve having a prescribed torsion group over some quadratic field and high rank. Their method rests on the formula \[ {\text{rank}}(E({\mathbb Q} ({\sqrt{d}})))={\text{rank}}(E({\mathbb Q}))+{\text{rank}}(E^{(d)}({\mathbb Q}), \] where \(E^{(d)}\) is the \(d\) quadratic twist of \(E\). When the torsion group \(T\) is also a torsion group of some curve \(E\) over \({\mathbb Q}\), the authors searched for curves \(E\) with prescribed torsion group \(T\) and a reasonable rank over \({\mathbb Q}\) and for a suitable twist \(E^{(d)}\) with a reasonable large rank such that \(E({\mathbb Q} ({\sqrt{d}}))\) does not acquire additional torsion. They found several interesting examples in this way, for example a curve with \(T={\mathbb Z}/12{\mathbb Z}\) and rank at least \(7\) (the highest rank over \({\mathbb Q}\) known for this \(T\) is \(4\)). For other groups such as \({\mathbb Z}/2{\mathbb Z}\times {\mathbb Z}/10{\mathbb Z}\) which do not appear as torsion groups of elliptic curves \(E\) over \({\mathbb Q}\) they started with a subgroup \(H\) of it (in this case \({\mathbb Z} /10{\mathbb Z}\)) and an elliptic curve \(E\) whose torsion over \({\mathbb Q}\) is \(H\) and searched for a twist with additional torsion points. In this way, they found interesting examples (of rank at least \(2\)) for all possible torsion groups except for \({\mathbb Z}/15{\mathbb Z}\) for which an example of rank at least \(1\) was already known and for which the authors do not have examples of larger ranks.