Non-abelian anyons are conjectured topological quasi-particles which shatter our understanding of quantum statistics. Exchanging two such quasi-particles can transform the quantum state in a way that cannot be undone without unwinding the exchange. The exotic properties of non-abelian anyons have puzzled researchers for decades, and the robustness associated with their statistics makes them an appealing platform for topological quantum computing. Despite broad research over the past decades, non-abelian anyons defy a conclusive experimental observation. The goal of NON-ABELIAN is the realization and exploration of non-abelian anyonic quasi-particles. We will focus on two paradigmatic systems: quasi-hole excitations in Pfaffian-type fractional quantum Hall states, and Majorana edge states in the Kitaev chain. In each system, we will use control on the microscopic level to prepare the many-body ground state, as well as to isolate, braid, and fuse its quasi-particles. Using local correlations and interferometric observables, we will reveal the properties, including their fractional charge and their non-abelian statistics. The experiments are carried out on a novel type of neutral-atom platform. It makes use of ultraprecise holographic beam shaping, programmable optical tweezer arrays, and rapid ground state cooling techniques. By studying the emergence of non-abelian quasi-particles in two complementary systems, this project will shed light on an elusive type of quasi-particle from new angles. This will lead to fundamental consequences on our understanding of quantum statistics and provide microscopic insights into strongly correlated topological systems. In addition, our experiments open avenues for topological quantum computing with cold atoms.