This paper presents a programmable quantum simulator based on two-dimensional arrays of neutral atoms, featuring strong interactions controlled via coherent atomic excitation into Rydberg states. The system, with tunable interactions, realizes a quantum spin model and supports system sizes ranging from 64 to 256 qubits. The authors benchmark the system by creating and characterizing high-fidelity antiferromagnetically ordered states and demonstrate the universal properties of an Ising quantum phase transition in (2+1) dimensions. They also create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation, experimentally mapping the phase diagram and investigating the role of quantum fluctuations. This work offers a new perspective on the study of complex quantum matter, paving the way for investigations of exotic quantum phases, non-equilibrium entanglement dynamics, and hardware-efficient realization of quantum algorithms. The experiments demonstrate that two-dimensional Rydberg atom arrays are a powerful platform for programmable quantum simulations with hundreds of qubits, with potential for further improvements in system size, quantum control fidelity, and programmability.This paper presents a programmable quantum simulator based on two-dimensional arrays of neutral atoms, featuring strong interactions controlled via coherent atomic excitation into Rydberg states. The system, with tunable interactions, realizes a quantum spin model and supports system sizes ranging from 64 to 256 qubits. The authors benchmark the system by creating and characterizing high-fidelity antiferromagnetically ordered states and demonstrate the universal properties of an Ising quantum phase transition in (2+1) dimensions. They also create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation, experimentally mapping the phase diagram and investigating the role of quantum fluctuations. This work offers a new perspective on the study of complex quantum matter, paving the way for investigations of exotic quantum phases, non-equilibrium entanglement dynamics, and hardware-efficient realization of quantum algorithms. The experiments demonstrate that two-dimensional Rydberg atom arrays are a powerful platform for programmable quantum simulations with hundreds of qubits, with potential for further improvements in system size, quantum control fidelity, and programmability.