Analytical Mechanics

<p>This textbook is based on the author's lecture notes held at Qiuzhen College Tsinghua University Beijing renowned for its rapid scientific growth of its excellent students. The book offers a remarkable combination of characteristics that are both exceptional and seemingly contradictory. It is designed to be entirely self-contained starting from the basics and building a strong foundation in geometric and algebraic tools. Simultaneously topics are infused with mathematical elegance and profundity employing contemporary language and techniques. From a physicist's perspective the content delves deeply into the physical aspects emphasizing the underlying principles. This book bridges the gap between students and cutting-edge research with a special focus on symplectic geometry integrability and recent developments in the field.  It is designed to engage and captivate the reader. A conscious selection of topics ensures a more relevant and contemporary approach compared to traditional textbooks. The book addresses common misconceptions offering clarity and precision. In its quest for brevity this book is tailored for a one-semester course offering a comprehensive and concise resource. The author's dedication is evident throughout this volume encapsulating these goals within roughly 300 pages.</p>