Magnetism in materials is one of the oldest scientific discoveries, but is still far from being completely understood. I am proposing to use new and, as yet, completely unexploited experimental techniques to learn about materials where the magnetic interactions act to make the magnetic state stable; but only just stable! This means that small changes in the environment can cause dramatic changes in the magnetic properties. I propose to investigate these effects with muons. These are subatomic particles that may be implanted into materials where they act as microscopic magnetometers. In a solid, the atoms interact with each other through electrostatic forces between the electrons attached to the atoms. These forces are short range, so an atom is only on speaking terms with it neighbours. Electrons have a property known as spin, which is best thought of as an arrow attached to each electron. At high temperatures the spins on are randomly aligned, but as we reduce the temperature the electrostatic interactions cause the spins to line up with those of their neighbours. Amazingly, short range forces act to make all of the spins in the solid align. From local atoms speaking only to their neighbours, we have created collective action in the form of long-range order. Long-range order is seen throughout nature and the theory of such order explains the clustering of galaxies, the distribution of earthquakes, the spread of disease and even the very existence of the universe itself. A crucial factor in magnetism is the way in which interactions pass information (like line up spins this way'') between atoms. There may be situations where the interactions only act along a line of atoms (one-dimension) or in a plane of atoms (two-dimensions). This dimensionality is at the root of the behaviour of all long-range ordered systems. This is far from being a theoretical abstraction - it is possible to make 1D and 2D materials in the laboratory. Here, molecules are often employed as the building blocks of the materials rather than individual atoms. These molecular magnets are self assembled nanostructures, formed from networks of magnetic metal atoms which are linked together using organic molecules. The great number of organic molecules allow us to make small changes to the structure of magnets leading to tailor made materials with desired properties.Another important class of magnet results when messages sent to an atom conflict, a phenomenon known as frustration . If each atom is receiving conflicting instructions as to which direction is should align, it is not obvious which it will obey. It is therefore difficult to predict the ground state of the system (that is, the state adopted at very low temperatures). The investigation of such systems provide insights into why materials adopt the states that they do. Why should a certain material be a ferromagnet while another stays disordered down to low temperature? We can even gain an insight into why the solid state itself is stable.I propose to carry out research into frustrated and low-dimensional materials using muons. These are a subatomic particle that may be implanted in a material in order to measure the internal magnetic field. Investigations with muons reveal properties invisible to other, more conventional, experimental techniques. Both frustrated and low-dimensional materials tend to exist at the edges of stability, so that small changes in their external environment lead to dramatic changes in their behaviour. This means that experiments where small perturbations are applied to on of these magnets tend to yield much interesting information about their behaviour. New experimental techniques have recently been developed where perturbations may be applied and simultaneous measurements made with muons. These, as yet, have been completely unexploited in front line research and it is their first deployment that forms the basis of my work.