In the past years,  setups  based on atoms trapped in an array of optical tweezers and excited into Rydberg levels have emerged as a very powerful tool for quantum simulation of many-body systems. In this talk, an introduction into Rydberg atoms and their potential for quantum simulations is presented, as well as  the basic theoretical concepts are introduced.  As an application, we present the realization of a symmetry protected topological phase of interacting bosons in a one-dimensional lattice, and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states using such a setup based on Rydberg atoms.