"In chapter 1 we present some historical review of the interferometry in general and in particular an introduction to the Lateral Shear Interferometry (LSItry). Some shearograms produced by aberrations of third order in the Lateral Shear Interferometer (LSI) are exhibited. A little information about the LSItry is presented in an introductory way. The chapter 2 is concern with the basis of the interference, aspects of coherence of electromagnetic waves that superpose in space. An example of two plane waves that interfere in space is developed using a vectorial description. Chapter 3 studies the Lateral Shear Interferometer (LSI), third-order primary aberrations are developed for the LSI; this set of equations can be used to calculate the shearogram produced by this kind of interferometer. A complete study of the Murty’s interferometer is developed. Regarding about its parameter to be used to design are showed and demonstrated. Some characteristics of the Lateral Shear Interferometer like the frequency response are shown; the LSI like a linear system and the sensitivity of the LSI respect to the displacement is also calculated. In chapter 4 we study the estimation of the wave-front from maps of phase lateral sheared unwrapped, this chapter pretend to explain the effects of try to recover the wave-front from simple inverse transfer function. The least squares integration for lateral displacements greater than one CCD pixel produce a matrix that can’t be inverted, in this case, to yield a stable solution the regularizing potentials are a must. A particular case is studied, i.e. with little shearing, the method of Fried-Hudgin for integrating field of gradient, has a welldefined and unique minimum. Therefore it is not necessary to regularize the problem for one CCD pixel lateral shearing. Introducing higher lateral shearing is better to increase the sensitivity of the measurement. In chapter 5 we review the loss of information due to a large lateral shearing in the LSI. The effect of the pupils is that there is loss of information due to exist points on the wave-front that don’t interfere with another point of the wavefront, so on that point is truncated from the observations and must be interpolated by a priory knowledge. This information is reconstructed from the regularizing potentials acting like a low-pass filter, i.e. smoothing the data observed. In chapter 6 are shown several results in one dimension of the recovery of the wave-front."