This volume contains a collection of papers in analytic and elementary number theory in memory of Professor Paul Erdos, one of the great mathematicians of the 20th century. Written by many leading researchers, the papers deal with advances in a wide variety of topics, including arithmetical functions, prime numbers, the Riemann zeta function, probabilistic number theory, properties of integer sequences, modular forms, partitions, and q-series. The text should be of interest to researchers and students of number theory, analysis, combinatorics and modular forms.