\part{Fundamentals}


linear algebra
group theory


\chapter{Representations}


Category theory can be used to extend the notions to more algebraic structures.

representation
$(V,\rho)$ where $\rho : A \to \mathrm{End}(V)$ is a homomorphism
$(V,\rho)$ where $\rho : G \to \mathrm{GL}(V)$ is a homomorphism

irreducible representation

indecomposable representation

\begin{lemma}[Schur's lemma]
\end{lemma}

\chapter{Character theory}