Topology Courses and Certifications

ICTP Mathematics

Four-Manifolds with Boundary and Fundamental Group Z

Explore advanced concepts in geometry and topology, focusing on four-manifolds with boundary and fundamental group Z, presented by MIT expert Lisa Piccirillo.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Topological Spaces and Manifolds - Differential Geometry Lecture 24

Explore topological spaces and manifolds through neighborhood systems and open sets. Learn key concepts, solve problems, and understand the foundations of continuous space theory in modern mathematics.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Michael Penn

The Strangest Circle - Mathematical Curiosities and Paradoxes

Explore a fascinating mathematical concept: a circle with peculiar properties that challenge conventional geometry, offering unique insights into advanced mathematical thinking.

• YouTube
• 31 minutes
• Self-Paced
• Free Video

IIT (ISM) Dhanbad;  NPTEL

Essentials of Topology

Explore foundational mathematics, delving into topological spaces, connectedness, compactness, and separation axioms. Develop a deeper understanding of mathematical concepts beyond computational exercises.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course

Point Set Topology

Explore fundamental concepts in point set topology, including topological spaces, continuous maps, metric spaces, connectedness, compactness, and metrization, with a focus on practical examples from mathematics.

• Swayam
• 8 weeks
• Available until Sep 11, 2026
• Free Online Course

An introduction to Point-Set-Topology Part - II

Explore advanced point-set topology concepts, including compactness, paracompactness, metrization theorems, and function spaces. Develop a deeper understanding of topological properties and their applications in mathematics and physics.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course

The Royal Institution

Linking and Knotting - 1978 Christmas Lectures 1/6

Explore topology through linking and knotting in this classic 1978 mathematics lecture, covering mathematical proofs, Möbius strips, and DNA structure applications.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Homotopy Theory, Manifolds, and Field Theories

Explore advanced topics in homotopy theory through expert lectures on elliptic cohomology, factorization homology, and moduli spaces of manifolds from leading mathematicians.

• YouTube
• 14 hours 55 minutes
• Self-Paced
• Free Video

Michael Penn

A Complete Explanation of Hausdorff Spaces - Live Example

Discover the fundamental properties of Hausdorff spaces through clear explanations and practical examples in this concise topology lesson.

• YouTube
• 12 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Heegaard Floer Homology

Dive into Heegaard Floer homology through comprehensive lectures covering fundamental concepts and advanced applications in low-dimensional topology and knot theory.

• YouTube
• 3 hours 53 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Twisted Topological Tangles or- The Knot Theory of Knitting - Elisabetta Matsumoto

Explore the fascinating intersection of knot theory and knitting, delving into topological properties, elasticity, and mathematical models that unravel the complexities of fabric structure.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Graph Reconstruction via Discrete Morse Theory

Explore graph reconstruction using discrete Morse theory, focusing on geometric graphs and density data. Learn about theoretical guarantees and applications in road network reconstruction.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

International Mathematical Union

Homotopy Patterns in Group Theory

Explore homotopy patterns in group theory, delving into advanced mathematical concepts and their applications in topology and algebra.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Shapes and Geometry of Surfaces by Mahan Mj

Explore the fascinating world of surfaces and their geometric properties. Learn about classification, topology, and curvature in this comprehensive lecture on shapes in space.

• YouTube
• 1 hour 47 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Basic Homotopy Theory by Samik Basu

Explore fundamental concepts in homotopy theory, including maps, CW complexes, equivalences, and fibrations. Gain insights into key computations and sequences in this foundational area of topology.

• YouTube
• 56 minutes
• Self-Paced
• Free Video