This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics.

Generalized Ramanujan primes.- Arithmetic congruence monoids: A survey.- A short proof of Kneser's addition theorem for abelian groups.- Lower and upper classes of natural numbers.- The probability that random positive integers are 3-wise relatively prime.- Sharpness of Falconer's estimate, and the single distance problem in Z^d_q.- Finding and counting MST sets.- Density versions of Plünnecke inequality: Epsilon-delta approach.- Problems and results on intersective sets.- Polynomial differences in the primes.- Most subsets are balanced in finite groups.- Gaussian Behavior in Generalized Zeckendorf Decompositions.- Additive number theory and linear semigroups with intermediate growth.- Adjoining identities and zeros to semigroups.- On the Grothendieck group associated to solutions of a functional equation arising from multiplication of quantum integers.- The Plünnecke-Ruzsa inequality:An overview.- Lerch Quotients, Lerch Primes, Fermat-Wilson Quotients, and the Wieferich-non-Wilson Primes 2, 3, 14771.- On sums related to central binomial and trinomial coefficients.

This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems, and future challenges in number theory.