Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. As a result, they are subject to the Pauli exclusion principle and obey Fermi-Dirac statistics. The spin-statistics theorem states that fermions have half-integer spin. One possible way of visualizing spin is that particles with a 1/2 spin, i.e. fermions have to be rotated by two full rotations to return them to their initial state.
All elementary particles are either fermions or bosons. Composite particles composed of fermions may be either bosons (such as mesons) or fermions (such as baryons) depending on their total spin.
The elementary particles which make up matter are fermions, belonging to either the quarks (which form protons and neutrons) or the leptons (such as electrons). The Pauli exclusion of fermions is responsible for the stability of the electron shells of atoms, making complex chemistry possible. It also allows the stability of degenerate matter under extreme pressures.
Examples of fermions: