Quantum Mechanics describes the behaviour of matter on sub-microscopic scales and, together with relativity, is one of the two foundations of modern physics. Quantum systems are often described as having both wave-like and particle-like aspects to their behaviour, and are famous for producing results that defy common-sense intuition based on observations at everyday scales. In this module we will introduce Schrödinger's wave equation and use it to investigate the behaviour of simple quantum systems, from a free particle through to single-electron atoms. We will discuss the wavefunction, which describes the state of a system, how to interpret it, and how making a measurement changes the wavefunction. We will illustrate some of the non-intuitive behaviour of quantum systems, show how it arises, and how, in the limit of large energies, it tends towards classical behaviour. We will discuss how mathematical operators are used to represent physical quantities, and see where the Uncertainty Principle comes from. We will introduce the quantum treatment of angular momentum and show how an additional property of the electron (spin) is required to describe atomic states. We will consider the special properties of quantum states consisting of more than one electron, and show how the existence of complex chemistry depends on these.