Arithmetic Combinatorics (also formerly known as Additive Combinatorics) is a very popular area of research. In my opinion, what makes it extremely interesting is the very strong interaction between numerous fields such as: number theory, combinatorics, group theory, harmonic analysis, ergodic theory, and many more. There was tremendous progress in recent years, and both classical and modern viewpoints will be studied. Historically, additive combinatorics studies additive properties of subsets of the integers, or more generally, abelian groups. In the past 10 years, it has been partially extended to the non-commutative case, with many important applications in group theory and number theory. We will focus on purely additive combinatorics, studying the basic notions of the field, and some of the major results (Szemeredi’s Theorem, Erdos-Szemer ́edi conjecture, Green-Tao Theorem, Freiman’s Theorem, etc) and techniques involved in proving these (graph theoretic techniques, character theory and Fourier analysis, ergodic theory).