The book "Differentiable G-Manifolds" by Klaus Jänich provides a comprehensive introduction to the theory of G-manifolds, which are central to mathematics. It covers fundamental concepts such as principal orbits, singular orbits, and exceptional orbits, and explains the embedding theorem as well as the classification of special G-manifolds. The use of diagrammatic representations and concrete examples facilitates the understanding of this complex subject. The work also includes reports on knot manifolds and discusses important linearity theorems that are significant for analyzing actions on IRn with two-dimensional orbit spaces. Additionally, it addresses gaps in the dimensions of transformation groups and the symmetry degree of exotic spheres, making the book a valuable resource for students and professionals in the fields of mathematics and natural sciences.