Algebraic Topology
Doctoral study of shape up to deformation: homotopy, the fundamental group, and homology.
Dr. Igor Volkov
Research Fellow, Topology
Homotopy & the Fundamental Group
Shape up to continuous deformation.
Counting Holes with Homology
What homology measures about a space.
Homeomorphism: Topological Equivalence
When two shapes count as the same.
Common questions
Who is "Algebraic Topology" for?
It is written for learners at PhD level (Doctoral), and for anyone older who wants a clear refresher on mathematics. Doctoral study of shape up to deformation: homotopy, the fundamental group, and homology. There is no application or entry test — you can start the first lesson straight away.
How long does the course take?
There are 3 lessons totalling 31 minutes of reading and quizzes, laid out over 2 units. You can move at your own pace — progress is saved as you go.
What do I need to know before starting?
No prior coursework is assumed. The course opens with "Homotopy", covering deformation and homotopy equivalence, so the foundations are built in rather than expected.
Is the course free?
Yes. Every course on Monster Class is completely free, with no credit card, trial period or paywall. Creating a free account simply saves your progress, XP and place on the leaderboard across devices.