This textbook, the first volume of a two-part series, is based on the Mathematics 160 course taught at the California Institute of Technology for over 25 years. It offers an introduction to analytic number theory, tailored for undergraduates who are familiar with advanced calculus but have little to no background in number theory. The content is accessible, with much of it requiring little or no calculus, making it appropriate for high school students with a keen interest in mathematics. Number theory is a vast field, and it's impossible to cover everything in a single course. This book provides a carefully selected range of topics that balance both breadth and depth, featuring classical problems that have intrigued mathematicians for centuries. It also introduces the essential techniques used to solve these problems. One of the main objectives of this course-and this book-is to cultivate a deeper interest in number theory among students, while also opening doors for them to explore more advanced research in the field. The author has been fortunate to see many former students, after taking this course, go on to become professional mathematicians, with several making notable contributions to number theory.