Here are some notes I wrote. I would be very happy if this helps anyone.
An Introduction to Representation of Finite Groups
This is my notes based on a small section (representation theory part) of Prof. Dima Arinkin's course Abstract Algebra I (Madison 2025 Fall).
An Introduction to Homological Algebra
This is my notes based on Prof. Andrei Căldăraru's course Homological Algebra (Madison 2025 Fall). The content covers basic topics in derived functors and derived categories.
This is my notes based on Prof. Jeremy Hahn's course Simplicial Homotopy Theory (Cambridge Part III 2025 Lent). The content covers basic topics in infinite categories and homotopy theory of Kan complexes.
An Introduction to Characteristic Classes
This is my reading report on characteristic classes at the University of Liverpool. They are mainly based on Bott and Tu's book Differential Forms in Algebraic Topology. The content covers basic concepts in differential geometry and algebraic topology, along with an introduction to characteristic classes.