The paper by S. L. Woronowicz explores non-commutative differential geometry, focusing on the development of differential calculus on quantum groups. The author introduces bicovariant bimodules, which are analogous to tensor bundles over Lie groups, and describes constructions of tensor and exterior algebras. Key results include the natural lifting of first-order differential calculi to the exterior algebra, ensuring well-defined higher-order exterior derivatives. The Cartan-Maurer formula is properly formulated, and a bilinear operation is defined on the dual space of left-invariant differential forms, serving as the Lie bracket. The generalized antisymmetry relation and Jacobi identity are also established. The paper aims to generalize classical Lie group theory to the quantum group setting, emphasizing the importance of differential forms over vector fields in non-commutative geometry. The axiomatic method is used to introduce first-order differential calculus, and the paper discusses the correspondence between calculi and right ideals in the algebra of "smooth functions" on the quantum group. The second section delves into bicovariant bimodules, proving their topological triviality and introducing the adjoint representation. The third section focuses on the twisted flip automorphism, which enables the introduction of antisymmetrization operations on tensor powers of bicovariant bimodules.The paper by S. L. Woronowicz explores non-commutative differential geometry, focusing on the development of differential calculus on quantum groups. The author introduces bicovariant bimodules, which are analogous to tensor bundles over Lie groups, and describes constructions of tensor and exterior algebras. Key results include the natural lifting of first-order differential calculi to the exterior algebra, ensuring well-defined higher-order exterior derivatives. The Cartan-Maurer formula is properly formulated, and a bilinear operation is defined on the dual space of left-invariant differential forms, serving as the Lie bracket. The generalized antisymmetry relation and Jacobi identity are also established. The paper aims to generalize classical Lie group theory to the quantum group setting, emphasizing the importance of differential forms over vector fields in non-commutative geometry. The axiomatic method is used to introduce first-order differential calculus, and the paper discusses the correspondence between calculi and right ideals in the algebra of "smooth functions" on the quantum group. The second section delves into bicovariant bimodules, proving their topological triviality and introducing the adjoint representation. The third section focuses on the twisted flip automorphism, which enables the introduction of antisymmetrization operations on tensor powers of bicovariant bimodules.