Topological Data Analysis

An introduction to TDA based on Oxford lecture notes and Hatcher.
Lecture 1 , Lecture 2 , Lecture 3 , Lecture 4-5, Lecture 6, Lecture 7 :

Introduction to Algebraic Varieties

An introductory course based on my Oxford AG course. Lecture notes 

Algebraic Topology

First half of an  intro course based on Hatcher. 
Lecture 1 , Lecture 2 , Lecture 3 , Lecture 4 , Lecture 5 , Lecture 6, Lecture 7, Lecture 8, Lecture 9 , Lecture 10 , Lecture 11 , Lecture 12   

Symplectic Geometry

Intro course based on Ana Cannas da Silva's textbook.
Lecture 1 , Lecture 2 , Lecture 3 , Lecture 4 , Lecture 5 , Lecture 6 , Lecture 7 , Lecture 8 , Lecture 9 , Lecturer 10 , Lecture 11