  The paper aims at giving an introduction to the notion of quantum curves. The
main purpose is to describe the new discovery of the relation between the
following two disparate subjects: one is the topological recursion, that has
its origin in random matrix theory and has been effectively applied to many
enumerative geometry problems; and the other is the quantization of Hitchin
spectral curves associated with Higgs bundles. Our emphasis is on explaining
the motivation and examples. Concrete examples of the direct relation between
Hitchin spectral curves and enumeration problems are given. A general geometric
framework of quantum curves is also discussed.
