Explore a detailed mathematical lecture examining the various constructions of vertex algebras and their relationships to Lie superalgebras. Delve into three primary construction methods: standard bosonisation, reduction from affine Kac-Moody algebras, and extension. Learn about the fundamental phenomenon of isomorphism between algebras derived through different construction approaches and understand how this creates corresponding conformal theory isomorphisms. Gain advanced insights into coset vertex algebras and W-algebras, with particular emphasis on their connections to Lie superalgebras through this comprehensive mathematical discussion.