This contributed volume presents recent advances as well as new directions in number theory and its applications. Algebraic and analytic number theory are the main focus with chapters showing how these areas are rapidly evolving. By gathering authors from over seven countries, readers will gain an international perspective on the current state of research as well as potential avenues to explore. Specific topics covered include:Algebraic Number TheoryElliptic curves and CryptographyHopf Galois theoryAnalytic and elementary number theory and applicationsNew Frontiers in Number Theory and Applications will appeal to researchers interested in gaining a global view of current research in number theory.