The report describes the results of a theoretical study on the analysis and design of leading edge slat plus main airfoil combinations. Two basic methods were used: representation of the slat by a point vortex, and representation of the slat by a set of thin airfoil theory singularity distributions. Computer programs were prepared. For method 1 the main airfoil was chosen from an infinite set of airfoils whose mapping functions to the unit circle are analytically defined. A leading edge slat providing a specified velocity modulation on the nose region of a main airfoil was studied by method 2.