A varnish having low viscosity and a cured product thereof having a high degree of cross-linking, exhibiting excellent low dielectric properties and mechanical properties at high temperature, and a low coefficient of linear thermal expansion are provided. A varnish comprising an olefin-aromatic vinyl compound-aromatic polyene copolymerized oligomer satisfying specific conditions, one or more selected from the following (a) to (c), and (d) a solvent: (a) a curing agent; (b) one or a plurality of resins selected from a hydrocarbon-based elastomer, a polyphenylene ether-based resin, an olefin-aromatic vinyl compound-aromatic polyene copolymer, and an aromatic polyene-based resin; and (c) a polar monomer; and a cured product of the varnish.