The method of analytical continuation of the Schrodinger equation in the complex energy plane based on deforming the integration contour in momentum space is commonly known as the Contour Deformation Method. In this book the Contour Deformation Method and the rules for analytical continuation of integral equations are discussed in detail, and examples of simple scattering problems are given for the case of Yukawa like potentials. It is shown that the Contour Deformation Method can provide a simple means of constructing a complete single particle basis that treats bound, resonant and...