This chapter provides a description of atomic nuclei wholly in terms of their fermion degrees of freedom. An algebraic fermion model is a many-particle shell-model theory which treats nucleons within a nucleus as fermions and invokes special group symmetries associated with collective behavior in an attempt to achieve a tractable microscopic description of nuclear phenomena. The main difficulty in developing a many-particle shell-model theory stems from the fact that while many properties of the interaction between nucleons are known from nucleon-nucleon scattering data, their renormalization in the nuclear medium is not at all well understood. The many-particle shell-model scheme starts with a single-particle picture and adds nucleons to orbitals of the valence space subject to the constraint of the Pauli Principle. Significant progress towards bridging this gap between the macroscopic and microscopic pictures of nuclear structure has recently been made.