Critical currents and superconductivity : ferromagnetism coexistence in high Tc oxides Superconducting state Basic models Characteristics of high Tc superconductors Phenomenoligical theories of the anisotropic superconductors Dynamic of vortices Interactions vortex vortex vortex defect and vortex spin The field of superconductivity is constantly evolving. Very important discoveries were made since the beginning of the last century; some of them have even rewarded with Nobel Prizes. In 1911 K.H. Onnes discovered that the electrical resistivity of many metals vanishes below certain very low critical temperatures (Nobel Prize). In 1933 W. Meissner and R. Ochsenfelds showed that cooled to temperatures below its critical temperature a superconductor expels the magnetic field. In 1935 F. and H. London followed in 1950 by V.L. Ginzburg and L.D. Landau developed phenomenological theories which provided a better understanding of superconductivity (Nobel Prize). Based on these models A. Abrikosov presented in a theory of the mixed state of type II superconductors which stipulates that the magnetic flux penetrates in these materials in the form of vortices (Nobel Prize). The same year J. Bardeen L.N. Cooper and J.R. Schrieffers elucidated the physical causes of the superconductivity phenomenon (Nobel Prize). In 1962 B.D. Josephson explained the tunneling junction behavior between the superconductors (Nobel Prize). Around the same time the discovery of type II superconductors which support very high magnetic fields (20 teslas) led to their intensive use for the generation of strong fields. In 1986 J.G. Bednorz and K.A. Muller discovered superconductivity in a copper and lanthanum oxide doped with barium with a critical temperature of the order of 30 K (Nobel Prize). This was the beginning of the high TC superconductors era. The highest critical temperature reached to date is 133 K in a compound of the type HgBaCan 1CunO2n+2+d with n = 3 at ambient pressure