A microwave valve is considered as a three-dimensional waveguide in conjunction with an electron mechanism. Three spatial axes are chosen and the ways in which they can be terminated are studied. By allotting a symbol to each method of axis termination, all the possible circuit geometries for a given method of interaction can be obtained by permutation. The number of basic valve types is then obtained, after observing that the electron beam may be considered to be subject to the same methods of termination as the spatial axes. Initially 256 symbol groups are found, of which 108 are oscillators and 148 are amplifiers, but these 256 reduce to 104 when considerations of redundancy due to symmetry, of geometrical impossibilities and of the necessity for uniaxial power outflow, are taken into account.These 104 groups are all theoretically possible structures for amplifiers or oscillators, though as 68 contain a certain geometrical complexity which makes them less likely as practical arrangements, only the remaining 36 are considered further and discussed in conjunction with the main types of electron mechanism.The symbolism for many of the familiar valve types is quoted as illustration, but the possible value of the symbolism may lie in the prediction of properties of valves having the same symbol group but different electron mechanisms. An interesting group arises which may be described as “fast-wave” amplifiers, implying that no slow-wave circuit is necessary as with distributed amplifiers of the Kompfner-Pierce type.