This chapter introduces Adiabatic Quantum Computing (AQC) and highlights its potential as an alternative to the circuit model. We introduce, via numerical demonstration, the quantum adiabatic theorem, which asserts that a system will remain in its ground state provided the Hamiltonian changes slowly enough. This principle forms the basis of AQC’s approach, making it capable of addressing complex problems like determining the ground states of quantum many-body systems, or the extremum of a cost function. The chapter covers the technique of embedding a time-independent Hamiltonian in a time-dependent one, facilitating a transition from a simple, solvable system to a more complex target problem. By slowly evolving the system, the initial Hamiltonian’s ground state becomes the target Hamiltonian’s ground state. Additionally, the text explores its application in areas traditionally linked to the circuit model, like Grover’s algorithm. Theoretical concepts are demonstrated with practical examples. Lastly, the chapter examines geometric and topological phases generated by adiabatic evolution and explores their potential as a resource.