The detailed dynamics of an unstable free shear layer are examined for a gravitationally stable or neutral fluid. This first article focuses on the part of the evolution that precedes the first subharmonic interaction. This consists of the transformation of selectively amplified sinusoidal waves into periodically spaced regions of vorticity concentration (the cores) joined by thin layers (the braids), in which vorticity is also concentrated. The thin layers are the channels along which vorticity is advected into the cores, and the cores provide the strain which creates the braids. For moderately long waves an analysis is given of the braid structure as a function of time. For gravitationally stable shear layers at high Reynolds numbers, the local vorticity reaches such large values as to cause secondary shear instability on a small (length) and short (time) scale. A physical account of the primary instability and its self-limiting mechanism is used as a basis for a computation, which yields growth rates and maximum amplitude as a function of initial layer parameters. The computation supplies the wavelength of waves that grow to achieve the largest (absolute) amplitude. Finally, the model makes it clear that, in the absence of secondary instability, this initial phase of the nonlinear development of the layer contributes only a modicum of additional mixing, especially at high Reynolds numbers.