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This book provides an in-depth discussion of the evolution of machine translation from rule-based systems to advanced deep learning models and Large Language Models (LLMs). This comprehensive guide covers traditional approaches, Statistical Machine Translation (SMT), and the transformative impact of neural networks and transformers. It explores the practical applications of LLMs like GPT, addressing evaluation metrics and ongoing research challenges. Ideal for researchers, practitioners, and students in NLP and AI, this book bridges theoretical foundations with real-world applications, offering valuable insights into the future of machine translation technology to understand the full spectrum of machine translation advancements, from foundational theories to the latest generative AI technologies.