Course content

The course gives an introduction to geometry and topology, with emphasis on classical geometries, topological classification of surfaces, and differential geometry for Riemannian surfaces.

Learning outcome

After completing the course you

  • can describe axioms for planar geometry, and models realizing these in the hyperbolic, Euclidean and elliptic cases
  • can work with Möbius-transforms, as well as distances, angles and areas in hyperbolic geometry
  • know about topological, combinatorial and differentiable surfaces, and can classify combinatorial surfaces up to homeomorphism
  • can describe Riemannian metrics and curvature, by means of the first and second fundamental forms, as well as the Theorema Egregium
  • know about geodesic curves on Riemannian surfaces, and the Gauss-Bonnet theorem.

Admission to the course

Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

Overlapping courses


4 hours of lectures/exercises per week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.


Final written exam or final oral exam, which counts 100 % towards the final grade.

The form of examination will be announced by the lecturer by 15 October/15 March for the autumn semester and the spring semester respectively.

This course has 1 mandatory assignment that must be approved before you can participate in the final exam.

Examination support material

No examination support material is allowed.

Language of examination

Courses taught in English will only offer the exam paper in English. You may submit your response in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Aug. 12, 2022 4:30:37 AM

Facts about this course

Teaching language