This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications - like the use of congruence in scheduling of a round-robin tournament - are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual."Elementary Number Theory with Applications 2e" is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. It is loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises. It covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes. Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East.