Water is the most abundant liquid on Earth s surface. It is essential for life. Surprisingly, despite extensive studies, many of its properties remain to be explained. The aim of this project is to contribute to the understanding of water, by studying its anomalies in the metastable liquid state. A liquid should transform into vapour at its boiling point, or into a solid at its freezing point. However, it can be observed beyond these limits. It is then in a metastable state, separated from the stable phase by an energy barrier due to surface tension. The short lifetime of the liquid under such extreme conditions renders measurements particularly challenging. Nevertheless, we find them worth to undertake, because they will bring valuable information on its structure. Our proposal is twofold: in the negative pressure range, where the liquid is metastable with respect to the vapour, we will stretch water to a high degree by several methods, and measure the extension of its equation of state. This part is based on our knowledge of different techniques to obtain large negative pressures; we will use optical methods to access the physical properties. in the supercooled range, where the liquid is metastable with respect to the solid, we will develop new viscometers to measure the viscosity of supercooled liquid water under pressure. Our aim is not only to provide the missing viscosity data for supercooled water up to 300 MPa, but also to check its relation with translational and rotational diffusion, which can reveal a change in the liquid structure.