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The Hamiltonian formalism is a reformulation of classical mechanics in terms of the total energy of a mechanical system. This is expressed by a Hamiltonian function, which can be used to describe the state of the mechanical system in terms of position and momentum variables. Examples of Hamiltonian systems include the mathematical pendululum, the rotor, and the Solar System model. In Hamiltonian systems, chaos and stability often coexist. This lecture is a brief introduction to Hamiltonian dynamics, with emphasis on (in)stability and chaos. Some recent research resluts will also be discussed.