By global analysis we mean the theory of smooth manifolds and the differential-geometric structures defined on them. By differential-geometric structures we refer to vector fields and differential forms. In addition, the lectures on global analysis introduce the basic concepts of Lie groups and Lie algebras. Several lectures are devoted to the fundamental notions of Riemannian geometry. This field is supported by a rich body of literature. Below, we list the books whose exposition is most closely aligned with our lecture course.

Frank W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer-Verlag. In this book, the author provides a detailed exposition of the fundamental concepts of the theory of smooth manifolds. The approach to defining the tangent space of a manifold presented in this book is the closest to the one adopted in the lecture course. The book offers a mathematically rigorous treatment of the theory of manifolds and differential-geometric structures on them. At the same time, the theoretical material is accompanied by numerous examples, which facilitates the understanding of abstract concepts and methods.
Lawrence Conlon, Differentiable Manifolds, Second Edition, Modern Birkhäuser Classics. This book contains a detailed exposition of the theory of smooth manifolds. In addition, one of the chapters is devoted to Riemannian geometry. At the end of the book, a brief overview of the structure of principal bundles is provided.
Alfred Gray, Modern Differential Geometry of Curves and Surfaces with MATHEMATICA, CRC Press. The main part of this book is devoted to an extensive presentation of the theory of curves and surfaces in three-dimensional Euclidean space. In parallel, the author introduces the fundamental skills for working with the computer program Mathematica , which is used throughout the book to study curves and surfaces. One of the chapters (Chapter 23) is devoted to the structure of smooth manifolds and tensor fields on them.
Daniel S. Freed, Karen K. Uhlenbeck, Instantons and Four-Manifolds, Springer-Verlag. This book is more of a scientific monograph on the structure of the set of anti-self-dual solutions to the Yang–Mills equations than a classical textbook on the theory of smooth four-dimensional manifolds. The Yang–Mills theory is a gauge field theory with gauge group SU(2), that is, the group of 2×2 unitary matrices with determinant one. The Yang–Mills theory is used to describe the strong interactions in atomic nuclei. The study of anti-self-dual solutions to the Yang–Mills equations led S. Donaldson to the discovery of the so-called "fake" smooth structures on four-dimensional manifolds. The book provides a brief overview of this remarkable discovery. It is worth noting that Karen K. Uhlenbeck is a recipient of the Abel Prize (awarded by the Norwegian Academy of Science and Letters) for her contributions to the study of the structure of instantons. In addition, Karen K. Uhlenbeck has Estonian roots (for more details, see V. Abramov, P. Lätt, Karen K. Uhlenbeck, geomeetria ja matemaatiline füüsika).