We all learn in quantum mechanics lectures how to treat the spin of an electron using the Pauli matrices of an S=1/2 system. However, the magnetic properties of atoms in gas and in particular those in a solid-state environment or in molecules are often much more complex and interesting. We will begin by trying to understand what happens when the spin of a quantum system is larger than S=1/2 at which point ligand fields (crystal fields in solids) become important and lead to important effects such as magnetic anisotropy. We will then move from the treatment of a single spin system to coupled spins. How do you set up spin matrices for such a situation and how do you find solutions to those problems? We will discuss some experimental findings about spin chains on surfaces as studied by STM. If time permits we will try to apply the concepts of coupled spin systems to quantum computation.