This book brings the techniques from Vedic Mathematics and Trachtenberg System together. We have not attempted to do a comparative study of these techniques and make a judgment on which one is better. Instead we have simply, presented the techniques in a sequence that makes most sense. There are inherent strengths in these two approaches. While looking at all the speed improvement techniques, we have ensured that we focus on techniques for defect prevention and error minimization as well. Speed coupled with improved accuracy must be our paramount focus during any problem solving process. This book attempts to elucidate several key techniques, examples and practice problem sets.