Organic superconductors: The (TMTSF)2X family

This review article is intended to give an elementary introduction to the basic theoretical understanding of the Quasi-One-Dimensional electron gas in organic conductors. It provides a simple theoretical picture of the electron gas instabilities arising at low temperature. Furthermore it gives a survey of the salient experimental results related on the one hand to the Peierls (insulating) instability of TTF-TCNQ and on the other hand to the superconducting instability recently discovered in the family of (TMTSF)2X conducting salts. Special emphasis is put on the consequence of One-Dimensionality for the existence of precursor regimes of the low temperature phase transitions up to temperatures much higher than the phase transition temperatures.