Large language models (LLMs) have fundamentally transformed how machines process and generate information. They are reshaping white-collar jobs at a pace comparable only to the revolutionary impact of personal computers. Understanding the mathematical foundations and inner workings of language models has become crucial for maintaining relevance and competitiveness in an increasingly automated workforce. This book guides you through the evolution of language models, starting from machine learning fundamentals. Rather presenting transformers right away, which can feel overwhelming, we build understanding of language models step by step—from simple count-based methods through recurrent neural networks to modern architectures. Each concept is grounded in clear mathematical foundations and illustrated with working Python code. In the largest chapter on large language models, you'll learn both effective prompt engineering techniques and how to finetune these models to follow arbitrary instructions. Through hands-on experience, you'll master proven strategies for getting consistent outputs and adapting models to your needs.