This dissertation describes the development, implementation, validation, optimization, and application, of a noninvasive and quantitative method for measuring cerebral blood volume changes with functional magnetic resonance imaging (fMRI) for mapping of neural activity changes. Since its inception over twenty years ago, the field of fMRI has grown in usage, sophistication, range of applications, and impact. Nevertheless it has yet to exploit its full potential regarding, spatiotemporal resolution, signal specificity, and quantifiability of hemodynamic changes. By utilization of a new MR pulse sequence, new concepts of radio frequency pulses, and high magnetic fields (7 T), a novel fMRI method named SS-SI VASO is presented here that overcomes sensitivity limitations of other noninvasive quantitative imaging methods. In order to validate that its signal represents changes in cerebral blood volume without other contaminations, SS-SI VASO is implemented in animal models for a close comparison with established, but invasive methods. A good agreement of blood volume sensitivity has been found with the new method compared to the established ones. After its validation, the SS-SI VASO method and its unprecedented sensitivity was used to localize and quantify hemodynamic changes in applications where conventional oxygenation based fMRI methods are limited. (A) SS-SI VASO was used to investigate biophysical aspects of actively controlled arteries and passive balloon-like veins during activity induced hemodynamic changes. (B) SS-SI VASO was used to provide insights whether the interplay of neural activity and resultant vascular response are the same for tasks that increase neural activity compared to tasks that suppress neural activity. (C) SS-SI VASO was used to calibrate conventional oxygenation based fMRI to quantify local changes in oxygen metabolism. (D) The high sensitivity of SS-SI VASO was further used to obtain sub-millimeter resolutions and estimate activity changes between cortical layers. This enables to address questions not only where the brain is activated but also how and whereby this activity is evoked. The implementation and application of this new SS-SI VASO fMRI method is a major step forward for the field of imaging neuroscience; it demonstrates that the current limitations of fMRI can be even overcome with respect to quantifiability, spatial specificity and distinguishing between vascular and neuronal phenomena.