This graduate level textbook is devoted to understanding, prediction and control of high dimensional chaotic and attractor systems of real life. The objective is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high dimensional chaotic and attractor dynamics. From introductory material on low-dimensional attractors and chaos, the text explores concepts including Poincare s 3-body problem, high-tech Josephson junctions, and more.