  These notes give an informal and leisurely introduction to $\mathrm{G}_2$
geometry for beginners. A special emphasis is placed on understanding the
special linear algebraic structure in $7$ dimensions that is the pointwise
model for $\mathrm{G}_2$ geometry, using the octonions. The basics of
$\mathrm{G}_2$-structures are introduced, from a Riemannian geometric point of
view, including a discussion of the torsion and its relation to curvature for a
general $\mathrm{G}_2$-structure, as well as the connection to Riemannian
holonomy. The history and properties of torsion-free $\mathrm{G}_2$ manifolds
are considered, and we stress the similarities and differences with Kahler and
Calabi-Yau manifolds. The notes end with a brief survey of three important
theorems about compact torsion-free $\mathrm{G}_2$ manifolds.
