We review the Renormalization Group from a physical view point and introduce the concept of beta function. We then introduce the basics of AdS/CFT with fermions. We show how to compute beta functions for double trace fermionic operators in the dual conformal field theory. We also describe a novel implementation of non-relativistic fermions in AdS/CFT by imposing Lorentz violating boundary terms for a Dirac spinor in AdS4. The dual boundary theory is scale invariant, and can be reached by an RG flow started by a Lorentz violating double trace perturbation. This new CFT exhibits a number of interesting properties, including a dispersionless flat band of gapless excitations.