0.1 Notation.

We use the standard (Bourbaki) notation:

Given an equivalence relation, $[\ast]$ denotes the equivalence class containing $\ast$. The cardinality of a set $S$ is denoted by $\left|S\right|$ (so $\left|S\right|$ is the number of elements in $S$when $S$ is finite). Let $I$ and $A$ be sets. A family of elements of $A$ indexed by $I$, denoted by $(a_{i})_{i\in I}$, is a function $i\mapsto a_{i}\colon I\rightarrow A$. Throughout the notes, $p$ is a prime number: $p=2,3,5,7,11,\ldots$.

$\begin{array}[c]{ll}X\subset Y&X\text{ is a subset of }Y\text{ (not necessarily proper).}\\ X\overset{\smash{\lower 1.31395pt\hbox{{def}}}}{=}Y&X\text{ is defined to be }Y\text{, or equals }Y\text{ by definition.}\\ X\approx Y&X\text{ is isomorphic to }Y\text{.}\\ X\simeq Y&X\text{ and }Y\text{ are canonically isomorphic (or there is a given or unique isomorphism).}\end{array}$