A few key concepts are useful to understand before delving into explanations of how magnetic resonance (MR) images are constructed and how we can use them to map neural function, because these concepts come up repeatedly or have an overall in¥uence over the theory and practice of functional magnetic resonance imaging (fMRI). One very in¥uential factor is the construction of the MRI system itself, because it determines the limited space and environment that we have to work within. Another important concept to understand is how numerical data can be represented as images, since all of the data used for fMRI are in the form of images. Furthermore, important mathematical concepts that occur throughout the theory of how images are constructed, and how they are analyzed, are based on the common idea of representing data as a sum of meaningful components.  ese concepts include separating data into components (such as with simple linear Ÿtting), the general linear model (GLM), and the Fourier transform. Although the level of detail presented in this chapter might go beyond what is needed to use these ideas for fMRI in practice, some readers may want to know the details, and so they are included here.