This thesis is a study of the affect of differences in the density of a fluid on the mixing regions of jets, which may be laminar or turbulent. These differences in density are present for three main reasons, namely; when the speed of the fluid is of the same order of magnitude as the local speed of sound; when there are large temperature differences in the fluid; and when the fluid consists of a mixture of components the relative proportions of which vary from point to point. Three problems are considered. These are: the flow far from the orifice of a plane and of a round jet and the mixing region on the surface of the core of a plane jet near the orifice. This last problem is idealised as the mixing of two semi-infinite streams. For flows of jet type, the assumption of a coefficient of eddy kinematic viscosity in turbulent flow leads to the possibility of combining in one the equations for laminar and turbulent motion. The method used is to expand the stream function in a Rayleigh-Jansen series. The first term of this series corresponds to the stream function when the fluid is of constant density. The series is developed in powers of a small parameter whose magnitude depends on the density differences in the fluid. Only the second term of this series is found explicitly. This term gives the first order effect that changes in density have on the flow. The solutions of all examples considered are, with on exception, given in analytical form. The last appendix to the the thesis shows the connection between Stewartson's (1957) approach to the problem of finding uniformly valid approximate solutions to the boundary layer equations and Lighthill's (1948) method. This connection is shown by working out one of the problems considered by Stewartson, namely, the wake past a flat plate, using Lighthill's method.