  Young diagrams are ubiquitous in combinatorics and representation theory.
Here we explain these diagrams, focusing on how they are used to classify
representations of the symmetric groups $S_n$ and various "classical groups":
famous groups of matrices such as the general linear group
$\mathrm{GL}(n,\mathbb{C})$ consisting of all invertible $n \times n$ complex
matrices, the special linear group $\mathrm{SL}(n,\mathbb{C})$ consisting of
all $n \times n$ complex matrices with determinant 1, the group $\mathrm{U}(n)$
consisting of all unitary $n \times n$ matrices, and the special unitary group
$\mathrm{SU}(n)$ consisting of all unitary $n \times n$ matrices with
determinant 1. We also discuss representations of the full linear monoid
consisting of all linear transformations of $\mathbb{C}^n$. These notes, based
on the column This Week's Finds in Mathematical Physics, are made to accompany
a series of lecture videos.
