We develop a general theory of W-algebras in the context of supersymmetric
vertex algebras. We describe the structure of W-algebras associated with odd
nilpotent elements of Lie superalgebras in terms of their free generating sets.
As an application, we produce explicit free generators of the W-algebra
associated with the odd principal nilpotent element of the Lie superalgebra
gl(n+1∣n).Comment: 24page