List of Free Online Geometry Courses and Lessons

Jan 02, 2019

Online Geometry Courses for Credit

Free courses in geometry that are accessible without registration or tuition are available online, though these courses do not provide college credit. If credit is important to you, you might check out the comparatively inexpensive content found on, which allows students to earn a certificate or begin the path to earning college credit while learning through engaging video lessons. These lessons also come with resources such as text transcripts and self-assessment quizzes.

Students looking to brush up on high school-level geometry can consider taking Geometry 101: Intro to Geometry, which includes chapters like:

  • Foundations of Geometry - Refresh your knowledge of inductive and deductive reasoning as well as the axiomatic system, undefined terms of geometry, and more.
  • Similar Polygons - Review ratios and proportions, the geometric mean, the transitive property of similar triangles, and related principles.
  • Analytical Geometry - Learn about using the midpoint formula, calculating the slope of a line, and geometric proofs for polygons.

Online Course Requirements and Information

Free online geometry courses offered through OpenCourseWare programs may help students with strong technical math backgrounds who are pursuing careers in mathematics or engineering. Courses from Open University include full lecture texts, excerpts from textbooks and video clips, while MIT geometry courses include lecture notes and some assignments.

Open University

  • Geometry instructs students on the use and construction of circles, lines, curves, planes and other geometric objects. Concepts such as rotational symmetry and angle analysis are discussed. The course also defines various terms used in geometry. Students can use a protractor and a free software download, Geogebra, to complete optional activities.
  • Modelling Displacements and Velocities explores how vectors are converted from component form to geometric form and vice versa. The lecture notes can be downloaded in optional e-book or Word document formats, and class exercises are available.
  • Symmetry examines direct and indirect symmetry, rotations and reflections of plane figures. Students can learn about symmetry composites and Cayley tables. Some prior knowledge of geometry is recommended for this intermediate class.
  • Surfaces covers topics ranging from familiar shapes, such as cones and spheres, to more complex structures, such as the torus and the projective plane. Students learn to determine whether a surface is orientable and how to define its Euler characteristic. Sample problems with solutions are offered throughout the course readings.

Massachusetts Institute of Technology (MIT)

  • Differential Geometry is an undergraduate course that focuses on plane curves, hypersurfaces, planes and distances. Concrete aspects of geometry, with a concentration on curves, comprise the bulk of the lecture notes and assignments. Prior knowledge of basic and linear algebra is recommended.
  • Geometry and Quantum Field Theory is designed for undergraduates who understand differential geometry and advanced calculus. Lecture topics include quantum field theory, quantum mechanics and matrix integrals. The seven assignments in this course can be downloaded as PDF files.
  • Algebraic Geometry explores morphisms, sheaves and different types of schemes. Students taking this course may need a background in commutative algebra. The curriculum includes lecture notes and assignments, although there are no solutions for the assignments.
  • Geometric Combinatorics introduces students to discrete and computational geometry. Topics include crossing numbers, simplicial partitions, arrangements of lines and curves, allowable sequences and geometric graph theory.
  • Computational Geometry is an advanced graduate-level class intended for mechanical engineers. This course features in-depth analysis of geometric solids, curves and surfaces. Lecture notes and optional assignments are included.
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