This lecture covers the concept of redescription SVM, where data is transformed to be linearly separable in a redescription space, and the use of Hilbert spaces to solve nonlinear problems. It explains the definition of redescription space, the role of inner product spaces in Hilbert spaces, and the completeness and separability of Hilbert spaces. The lecture also discusses separable Hilbert spaces of interest, such as Euclidean spaces and spaces of square summable sequences and functions.