The provided text is the preface and table of contents for the book "Foundations of Differentiable Manifolds and Lie Groups" by Frank W. Warner, published as part of the Graduate Texts in Mathematics series. The book serves as a comprehensive introduction to the theory of differentiable manifolds and Lie groups, designed for graduate students with a background in algebra and analysis. It covers core topics such as differentiable manifolds, tangent vectors, submanifolds, implicit function theorems, vector fields, distributions, differential forms, integration, Stokes' theorem, de Rham cohomology, and the foundations of Lie group theory. The book also includes detailed proofs of fundamental theorems like the de Rham theorem and the Hodge theorem, and provides a rich set of exercises to reinforce understanding. The preface acknowledges the contributions of various individuals and institutions, and the contents section outlines the structure of the book, including chapters on manifolds, tensors and differential forms, Lie groups, integration on manifolds, sheaves, cohomology, and the Hodge theorem.The provided text is the preface and table of contents for the book "Foundations of Differentiable Manifolds and Lie Groups" by Frank W. Warner, published as part of the Graduate Texts in Mathematics series. The book serves as a comprehensive introduction to the theory of differentiable manifolds and Lie groups, designed for graduate students with a background in algebra and analysis. It covers core topics such as differentiable manifolds, tangent vectors, submanifolds, implicit function theorems, vector fields, distributions, differential forms, integration, Stokes' theorem, de Rham cohomology, and the foundations of Lie group theory. The book also includes detailed proofs of fundamental theorems like the de Rham theorem and the Hodge theorem, and provides a rich set of exercises to reinforce understanding. The preface acknowledges the contributions of various individuals and institutions, and the contents section outlines the structure of the book, including chapters on manifolds, tensors and differential forms, Lie groups, integration on manifolds, sheaves, cohomology, and the Hodge theorem.