The need for effective methods of generating information and ultimately knowledge from experimental data is increasingly acute, due to the fact that such data is being generated at a rapidly growing rate and that the data now comes in much more varied forms than even a few years ago. One way of thinking about data is through its "shape", i.e. about the geometry it caries through the existence of a metric on it. In these talks, we will discuss how one can measure and represent the shape of data using adaptations of methods of topology to point cloud data, or finite metric spaces. We will discuss the computational methodology, and illustrate with various examples.