"The fine structure constant α, the masses and magnetic moments of elementary particles like the electron or proton, and others are fundamental quantities which determine the basic structure of the universe. They can not be predicted by theory, but their precise determination is required to enable the comparison of theoretical models with experimental observations at the highest possible level. The improvement of these quantities beyond the present level of accuracy represents a significant challenge for modern metrology. We propose ambitious experiments and measurements to substantially improve the precision of a number of fundamental constants, namely the electron and proton mass, the fine structure constant α, the magnetic moment of the proton and of the bound electron, and the Q-value of the 3H-3He decay for an improved sensitivity limit in the determination of the electron-antineutrino rest mass. Using single-ion storage in a well-defined small volume with perfectly controlled electromagnetic fields for nearly unlimited periods of time, we will measure the eigenfrequencies of the particles with unprecedented precision in dedicated Penning traps. From those values, fundamental properties such as the magnetic moment, atomic and nuclear mass or, equivalent, binding energy can be extracted. This will reveal the strength of all interactions present in the quantum mechanical system. Our new results combined with established theories will yield values for fundamental constants like the electron mass and the fine structure constant α. In order to meet these challenges novel trap geometries, ultra-sensitive and low-noise single-ion detection techniques will be developed and combined with other technological advances in order to enable us to reach up to one order of magnitude improved values for the quantities mentioned above."