In this very interesting paper the authors study the construction of standardly stratified algebras, a notion studied in many papers recently. The main idea in the paper under review is the so-called stratifying system: Given two sets of modules over an algebra, say \(\{\Theta(1),\Theta(2),\dots,\Theta(n)\}\) and \(\{Y(1),Y(2),\dots,Y(n)\}\), where the \(Y(i)\) are required to be indecomposable. They are called a stratifying system of size \(n\) if \(\operatorname{Hom}(\Theta(j),\Theta(i))=0\) for \(j>i\), and there is an exact sequence \(0\to\Theta(i)\to Y(i)\to Z(i)\to 0\) for each \(i\) such that \(Z(i)\) is filtered by \(\Theta(j)\) with \(j<i\) and \(\text{Ext}^1(\Theta(k),Y(j))=0\) for all \(k\) and \(j\). Once a stratifying system is given, the endomorphism algebra of \(\bigoplus Y(i)\) is proved to be standardly stratified and has invertible Cartan matrix. In the paper the authors provide also an existence theorem for stratifying systems. In particular, stratifying systems for special biserial self-injective algebras are constructed in detail.