Development and applications of a highly flexible nonlinear spatial encoding system for magnetic resonance imaging Abstract: The goal of this thesis was to design implement and test a shielded matrix gradient coil for magnetic resonance imaging (MRI).<br><br>The design process addressed gradient strength flexibility magnetic shielding cooling electrical decoupling balance of force and torque and patient safety. These demands were fulfilled by designing two different coil element types which form a cylindrical coil configuration containing two main current carrying surfaces and a shared shielding surface. For manufacturing and handling reasons the coil elements were designed such that each coil element can be manufactured and tested individually. Scaling the dimensions of a whole body gradient coil to an insert coil led to a total of 7 rings with 12 elements each summing up to a total of 84 elements. The resulting modular design led to a successful patent application. All 84 coil element channels were manufactured in house using a powder bed ink jet head 3D printing technology and assembled with the water cooling.<br><br>Before integrating the realized matrix coil prototype into a 3T MRI environment its electrical and thermal behavior was characterized experimentally. The gradient strength eddy current behavior acoustic response and the resulting field maps were characterized within the scanner environment. Established imaging methods were implemented and the resulting images prove the successful realization and integration of the coil. In vivo imaging experiments were performed after a satisfying safety assessment.<br><br>The flexibility regarding the realizable nonlinear spatial encoding magnetic field (SEM) shapes of the realized coil prototype allows for novel imaging methodologies. This is demonstrated in this thesis by deploying such SEM for simultaneous multislice imaging. The simultaneous excitation of multiple slices with standard single band radio frequency pulses was explored. Additionally frequency shifting of signals from different slices was demonstrated which in principle allows for parallel imaging without additional information from radio frequency receiver array coils