A free-electron Fermi gas is a gas of electrons with spin https://www.w3.org/1998/Math/MathML" display="inline"> S = 1 / 2 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003606857/19698a40-dbd9-4f9a-9cb7-890a1d39adce/content/math8_1.tif "/> . A fermion is a particle with half-integer spin S such as the electron. A boson is a particle with integer spin https://www.w3.org/1998/Math/MathML" display="inline"> S ≥ 0 https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003606857/19698a40-dbd9-4f9a-9cb7-890a1d39adce/content/math8_2.tif "/> . By a gas is meant that there are no interactions between the particles making up the gas. Thus a Fermi gas can exhibit no phase transitions by itself. On the other hand, a free boson gas can exhibit an interesting quantum phase transition into a superfluid state, qualitatively similar to that of the superconducting state of a metal, called Bose-Einstein condensation . In contrast, an electron Fermi liquid would be a system containing electrons that do interact with each other. We will see in the last two chapters of this book that when such interactions occur, magnetic or superconducting transitions associated with the electrons can happen.