---
title: Geometry & Topology
description: Geometry and topology study the properties, shapes, and structures of spaces. Learners will understand geometric theorems, coordinate systems, and topological concepts like continuity, compactness, and properties preserved under continuous deformation.
category: mathematics
subcategory: geometry-and-trigonometry
difficulty: beginner, intermediate, advanced
url: /subject/geometry-and-topology
---

# Geometry & Topology

Geometry and topology study the properties, shapes, and structures of spaces. Learners will understand geometric theorems, coordinate systems, and topological concepts like continuity, compactness, and properties preserved under continuous deformation.

## Available Resources

1 Books • 5 Websites

## Websites

### 1. nLab

Collaborative wiki run by working mathematicians and physicists covering category theory, higher category theory, homotopy theory, and their uses in geometry and physics. It serves as a reference for precise definitions, key results, and literature pointers on advanced topics.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://ncatlab.org/nlab/show/HomePage

**Tags:** category-theory, higher-category-theory, homotopy-theory, algebraic-topology, mathematics-reference

### 2. Hatcher's Algebraic Topology (free PDF)

**Author:** Allen Hatcher

Allen Hatcher's standard graduate textbook, freely downloadable from Cornell, covering fundamental groups, homology, cohomology and homotopy theory, with CW complexes introduced in Chapter 0 and used throughout. Readers learn to build spaces from cells and compute their algebraic invariants.

**Difficulty:** Intermediate | **Price:** Free

**Link:** https://pi.math.cornell.edu/~hatcher/AT/ATpage.html

**Tags:** algebraic-topology, cw-complexes, homology, homotopy-theory, fundamental-group

### 3. geometry.org

geometry.org is a curated online hub for learning geometry and topology, offering tutorials, articles, definitions, and lecture notes. It also aggregates links to courses, problem sets, and geometry software to support study.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://geometry.org

**Tags:** websites, mathematics-statistics, mathematics

### 4. geogebra.org

GeoGebra.org is a free dynamic mathematics platform that combines geometry, algebra, calculus, and statistics through interactive applets. It provides tutorials, worksheets, and a large library of user-created resources and activities for exploring geometric concepts and beyond.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://geogebra.org

**Tags:** websites, mathematics-statistics, mathematics

### 5. topology.org

Topology.org is a curated resource hub for geometry and topology, offering tutorials, lecture notes, definitions, and curated links to core concepts and visualizations.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://topology.org

**Tags:** websites, mathematics-statistics, mathematics

## Books

### 1. Euclid's Elements

**Author:** Euclid

Sir Thomas Heath's translation of Euclid's Elements with extensive commentary; this Dover volume contains Books X–XIII. It covers incommensurable magnitudes and solid geometry, ending with the five regular solids, and shows readers classical axiomatic proof as Euclid built it.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0486600904?tag=edmonddante07-20

**Tags:** books, mathematics-statistics, mathematics

---

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