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Abstract
The recently discovered high-temperature superconductors have a number of very unusual properties. Not only is the superconducting transition temperature Tc much higher than ever achieved before, but evidence is now growing that they may also be unconventional superconductors. An unconventional superconductor is one which has fundamentally different symmetries from those of other superconductors. Previously unconventional superconductivity was known to occur only in the heavy-fermion systems, such as the compounds UPt3 and UBe13. This review examines the basic concepts of symmetry applied to superconductors. I show how conventional (s-wave) and unconventional (p-wave and d-wave) superconductors arise naturally from the spontaneous symmetry breaking which leads to superconductivity. I then discuss the key experiments which can test for unconventional superconductivity in the high Tc and heavy-fermion systems. These experiments include meal