Eberhard Zeidler's "Nonlinear Functional Analysis and its Applications. Part 1: Fixed-Point Theorems" is a comprehensive work that explores the theory and applications of fixed-point theorems. The book is structured around three key fixed-point theorems: Banach, Schauder, and Bourbaki–Kneser. It is aimed at mathematicians, engineers, and natural scientists, offering insights into applications in physics, mechanics, chemistry, biology, and economics. The author focuses on explaining the meaning and basic concepts of theorems rather than presenting them in their broadest generality. An appendix provides foundational tools from linear functional analysis to assist readers. Each chapter includes problems and a bibliography. The first section covers fundamental fixed-point principles, including the Banach and Schauder theorems, with applications to differential equations. The second section, "Applications of the Fundamental Fixed-Point Principles," includes chapters from 3 to 11, discussing generalizations of the Picard–Lindelöf and Peano theorems, implicit function theorems, and Newton's method. Chapter 6 introduces the Leray–Schauder principle, which is crucial for proving the solvability of equations. Chapter 7 discusses ordered Banach spaces and their role in fixed-point theory, with applications to various equations. Chapter 8 covers analytic bifurcation theory, while Chapter 9 focuses on multivalued mappings and fixed-point theorems. Chapter 10 discusses nonexpansive operators and iterative methods, and Chapter 11 introduces measure of noncompactness and condensing maps, along with the Bourbaki–Kneser theorem. The book concludes with a section on mapping degree and fixed-point index, forming the third part of the work.Eberhard Zeidler's "Nonlinear Functional Analysis and its Applications. Part 1: Fixed-Point Theorems" is a comprehensive work that explores the theory and applications of fixed-point theorems. The book is structured around three key fixed-point theorems: Banach, Schauder, and Bourbaki–Kneser. It is aimed at mathematicians, engineers, and natural scientists, offering insights into applications in physics, mechanics, chemistry, biology, and economics. The author focuses on explaining the meaning and basic concepts of theorems rather than presenting them in their broadest generality. An appendix provides foundational tools from linear functional analysis to assist readers. Each chapter includes problems and a bibliography. The first section covers fundamental fixed-point principles, including the Banach and Schauder theorems, with applications to differential equations. The second section, "Applications of the Fundamental Fixed-Point Principles," includes chapters from 3 to 11, discussing generalizations of the Picard–Lindelöf and Peano theorems, implicit function theorems, and Newton's method. Chapter 6 introduces the Leray–Schauder principle, which is crucial for proving the solvability of equations. Chapter 7 discusses ordered Banach spaces and their role in fixed-point theory, with applications to various equations. Chapter 8 covers analytic bifurcation theory, while Chapter 9 focuses on multivalued mappings and fixed-point theorems. Chapter 10 discusses nonexpansive operators and iterative methods, and Chapter 11 introduces measure of noncompactness and condensing maps, along with the Bourbaki–Kneser theorem. The book concludes with a section on mapping degree and fixed-point index, forming the third part of the work.