A general survey of non central distribution is given, beginning with well known definitions and expressions of the non central Student's distribution of which different alternatives are presented, for example in terms of the moments of a truncated normal distribution, and followed by the generalised n. c. t distribution. The explicit formulae of its moments and coefficients of skewness and kurtosis are derived, as well as approximations of the same for large values ofn (number of degrees of freedom). The above obtained expressions being comparatively difficult to handle, a transformation to normalise the non centralt distribution is found, and the general form of the corresponding approximate moments and coefficients, summarised in two main alternatives, one for γ1=0, and the other for γ2=0. Some special cases are then discussed with detail, and examples of possible applications are widely exposed. Other non central distributions are briefly considered, based on the distribution of semirange, studentised range and analogues of n.c.t, and finally the generalised T distribution, which opened the way for new lines of research and which will be the subject of a subsequent paper.