Chan H. Analytic Number Theory for Undergraduates 2009

Textbook in PDF format

This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression.
The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.
Facts about Integers
Arithmetical Functions
Averages of Arithmetical Functions
Elementary Results on the Distribution of Primes
The Prime Number Theorem
Dirichlet Series
Primes in Arithmetic Progression