This page explains in detail the interactions between the Superman series and the Batman
world's finest comics[]
March, 1941
issues 1-70[]
the cover of the first issue of world's finest comics
Superman
Batman
the first interaction between the two series is in world's finest comics wich was originally an anthology series that featured mainly Superman and Batman stories with both of them often appearing in the cover.
issues 71 onwards[]
Superman
Batman
after the comic was made regular-size it began chronicling the team-up adventures of Batman and Superman In order to retain the draw of Superman and Batman without giving them both full-length stories.
adventures of superman[]
Superman 
Batman
the first in-universe link between both series was in the adventures of superman radio show wich ocassionally featured batman and robin
batman v superman: dawn of justice[]
batman v superman:dawn of justice is a crossover between the two series.
license[]
both series are owned by dc comics