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Geometry Free Books


"Geometry" is a fundamental branch of "mathematics" that studies "shapes", sizes, points, lines, angles, and spaces. It helps us understand how objects relate to each other in both two-dimensional (2D) and three-dimensional (3D) forms. From measuring land to designing buildings and bridges, geometry has been an essential part of human development since ancient times. There are several branches of geometry, including Euclidean geometry, analytic geometry, and solid geometry. "Euclidean geometry" focuses on flat surfaces and basic figures like triangles and circles, while "analytic geometry" combines algebra and geometry using coordinates. Solid geometry deals with 3D shapes such as cubes, spheres, and cones. These concepts are widely used in architecture, art, engineering, and computer design, providing a foundation for modern science and technology.


Many "free geometry books" are available online for learners, these resources explain basic and advanced concepts with clear examples and practice exercises. In summary, geometry connects logic, measurement, and creativity, helping us analyze and build the world around us with accuracy and beauty.

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Free Geometry Books
Beginning in Algebraic Geometry - Clader, & Ross
This text introduces the core ideas of "algebraic geometry" in a clear, beginner-friendly way. It connects "polynomials", "geometric intuition", and "projective spaces" through simple explanations and examples, making it ideal for students starting their journey into modern geometry.
Combinatorial & Computational Geometry - Jacob Goodman
This textbook covers "discrete geometry", "geometric algorithms", and "computational complexity". The book presents research on polytopes, packing, covering, convexity, and algorithmic solutions to geometric problems. It bridges theoretical and practical approaches, offering insights for mathematicians and computer scientists working on low-dimensional geometry.
Computational Geometry: Methods & Apps - Jianer Chen
This text teaches key "computational geometry" techniques and "geometric algorithms". The book explains concepts like convex hulls, triangulations, and Voronoi diagrams with practical "algorithm design" examples, making it ideal for students, researchers, and professionals working in graphics, robotics, and spatial computing.
Convex Bodies and Algebraic Geometry - Tadao Oda
This text explains how "convex bodies" relate to "algebraic geometry" through "toric varieties". The book shows how lattice polytopes and combinatorial methods help describe, analyze, and classify complex algebraic structures, making the connections between geometry and algebra clear and accessible for advanced students and researchers.
Curves & Surfaces in Geometric Modeling - Jean Gallier
This book explains how "curves" and "surfaces" are used in "geometric modeling". The book covers parametric methods like Bézier and B-splines, showing how mathematical principles guide design, computer graphics, and CAD, making complex shapes accurate and easy to create.
Differential Geometry - Pinkall & Gross
This text introduces "differential geometry", "Riemannian geometry", and "geometric analysis" in a clear, accessible way. It explains curves, surfaces, tangent spaces, curvature, and geodesics with examples and exercises, making it ideal for students and researchers in mathematics, physics, and applied geometric modeling.
Advances in Discrete Differential Geometry - A. Bobenko
This text introduces "discrete differential geometry" and "geometric algorithms" for studying curves, surfaces, and nets. The book combines theory with practical "computational geometry" applications, making it ideal for students, researchers, and professionals working in computer graphics, geometric modeling, and applied mathematics.
Discrete Differential Geometry - Bobenko & Suris
This text explains how "differential geometry" concepts can be applied to "discrete structures". It introduces practical "geometric algorithms" for modeling curves, surfaces, and shapes, making it ideal for students, researchers, and professionals working in "computational geometry" and applied mathematics.
An Elementary Course in Synthetic Projective Geometry
This textbook introduces "projective geometry", focusing on "poles and polars", "conic sections", and fundamental geometric relationships. The book emphasizes understanding shapes and their properties without measurements, making it an accessible guide for students and enthusiasts eager to explore the foundations and principles of synthetic geometry.
Euclidean Plane and Its Relatives by Anton Petrunin PDF
It is about Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist. It covers Euclidean geometry and Non-Euclidean geometry.
Fractal Geometry - Kenneth Falconer
This book explains how "fractals" reveal complex "geometric structures" in nature and mathematics. Using "Hausdorff dimension" and measure theory, the book shows how self-similarity and scaling help analyze irregular shapes, providing tools to understand and model fractals in both theoretical and real-world applications.
Fractals EveryWhere - Michael Bransley
This book explains how "fractals" use "self-similarity" and simple rules to create complex patterns. The book covers "mathematics" and computational methods, showing how fractals model natural shapes and structures, and how they can be applied in computer graphics, science, and real-world problem solving.
From Geometry to Behavior - Hanspeter Mallot
This text explains how the brain uses "geometry" to understand space and guide "behavior". Hanspeter Mallot shows how perception, movement, and navigation are shaped by internal spatial models, linking ideas from "cognitive science" to real-world actions in humans and animals.
Functional Differential Geometry - Gerald Sussman
This text explains "differential geometry" in a clear and practical way by focusing on meaning rather than heavy formulas. It uses "computation" and functional thinking to make ideas like manifolds, curvature, and metrics easier to understand, especially for students of "physics" and applied mathematics.
Intro to Differential Geometry - Robbin & Salamon
This text clearly explains the foundations of "differential geometry" with a strong focus on "rigor" and structure. The book introduces manifolds, smooth maps, curvature, and geodesics in a logical way, making it ideal for students who want a solid "mathematical foundation" for advanced study.
Lectures on Geometry of Manifolds - Liviu Nicolaescu
This text introduces "differential geometry" and "manifold theory" in a clear, accessible way. It explains tangent spaces, Riemannian metrics, curvature, and geodesics with examples and exercises, making it ideal for students and researchers learning "geometric analysis" and modern manifold concepts.
Lectures on Symplectic Geometry - Cannas da Silva
This text is a beginner-friendly introduction to "symplectic geometry", explaining how geometry connects to "classical mechanics" and smooth spaces. Ana Cannas da Silva presents key ideas like symplectic manifolds and Hamiltonian systems in a clear, structured way, making the book ideal for graduate students and early researchers.
Metric Algebraic Geometry by Paul Breiding - PDF
This text explores how "algebraic geometry", "distance problems", and "optimization" come together. The book explains how geometric shapes defined by equations can be studied using distances and metrics, with applications in data science, computation, and real-world mathematical modeling.
Number Theory and Geometry - Alvaro Lozano-robledo
This book explains how "number theory" connects with "geometry" using "elliptic curves" and modular forms. The book shows how geometric ideas help solve arithmetic problems, making complex concepts in arithmetic geometry accessible for students and researchers interested in the intersection of numbers and shapes.
Quasi-projective Moduli Polarized Manifolds - E Viehweg
This text explains how "moduli spaces" of "polarized manifolds" can be understood using tools from "algebraic geometry". Eckart Viehweg presents key ideas and results that clarify the structure of these spaces, making the book an important reference for advanced mathematical study.
Techniques in Fractal Geometry - Kenneth Falconer
This text explains how "fractals" are studied using "Hausdorff dimension" and "geometric structures". The book introduces practical methods and examples to analyze complex, irregular sets, helping readers understand the size, shape, and patterns of fractals in mathematics and real-world applications.
The Axioms Of Descriptive Geometry by Alfred Whitehead
This textbook is cover "descriptive geometry", "axiomatic systems", and "logical foundations". The book presents a clear set of axioms forming the basis of geometry, emphasizing formal reasoning. It provides a concise, structured approach that influenced modern developments in geometry and mathematical logic.
The Fourth Dimension by Charles Howard Hinton - PDF
This text explores "higher dimensions", "spatial imagination", and "tesseracts". The book explains how a fourth spatial dimension could exist beyond our three-dimensional perception. Using analogies and exercises, it helps readers visualize four-dimensional objects, offering insights into mathematics, philosophy, and the limits of human perception.
The Fractal Geometry of Nature - Benoit Mandelbrot
This text explains how "fractals" reveal patterns in nature. Using "geometry" and "self-similarity", Mandelbrot shows how irregular shapes like coastlines, clouds, and mountains can be modeled mathematically, uncovering hidden order in complex natural forms and inspiring science, art, and technology.
The Geometry of Fractal Sets - Kenneth Falconer
This book explains how "fractals" have unique "geometric properties" and "self-similarity". Using concepts like Hausdorff dimension, the book shows how to analyze complex, irregular shapes, providing clear tools and examples to understand the structure and patterns of fractal sets in mathematics and nature.
The Legacy of Felix Klein - Hans-Georg Weigand, et al
This text explains how Felix Klein shaped "modern mathematics", transformed "geometry", and influenced "mathematics education". Hans-Georg Weigand presents Klein as both a brilliant mathematician and an educational reformer whose ideas continue to guide mathematical thinking and teaching today.
The Story of Euclid - W. B. Frankland
This text explores the life and work of "Euclid", the father of "geometry". The book explains his influential "Elements", highlights his contributions to "mathematical reasoning" and "proof", and shows how his ideas shaped centuries of "mathematics" and logic in a clear, accessible way.
Wavelet Analysis on the Sphere - Arfaoui et al.
This text explains "wavelet analysis", "spherical harmonics", and "spherical wavelets" for data on curved surfaces. It shows how to build wavelets using orthogonal polynomials, helping scientists and engineers analyze signals and functions on spheres effectively.

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