This book is intended for all those who wish to understand, master and put into practice the principles, methods and tools for analyzing and simulating Automatic Hybrid Translation Systems (AHTS), in order to contribute to providing solutions in terms of model, performance and of overall quality. After an analytical and comparative presentation of the basic concepts and modeling tools in Machine Translation (MT); it performs a synthesis on the contribution of techniques of the Statistical MT approach based on ambiguous symbolic and context-free translation rules by exploiting statistical models, and that of the Neural MT approach which uses no explicit translation rules and is based on a single large neural network which relies on phrase-based systems basically exploiting two probabilistic models. Through several concrete examples, the analysis and simulation of our AHTS illustrates the effectiveness of the new neuro-statistical metamodel, for a hybrid and unified modeling of MT dynamic systems. It is a methodological tool intended for designers and users of MT system applications, students, teachers and researchers in applied computer science and computational linguistics.