  We provide an expository introduction to $\mathbb{A}^1$-enumerative geometry,
which uses the machinery of $\mathbb{A}^1$-homotopy theory to enrich classical
enumerative geometry questions over a broader range of fields. Included is a
discussion of enriched local degrees of morphisms of smooth schemes, following
Morel, $\mathbb{A}^1$-Milnor numbers, as well as various computational tools
and recent examples.
  Based off lectures delivered by Kirsten Wickelgren at the 2018 LMS-CMI summer
school ''Homotopy Theory and Arithmetic Geometry, Motivic and Diophantine
Aspects.''
