The physical properties of the heavy fermion compound CeNi2Ge2, have been investigated in this dissertation. Although heavy fermion systems are strongly correlated electron systems with hybridization of conduction and f-electrons, they usually still follow a Landau Fermi liquid description with high renormalized fermion masses. Modifying the electron correlations by chemical substitution or pressure, heavy fermions can be driven through a magnetic quantum critical point changing, e.g., from a magnetic ordered into a nonmagnetic ground state. Close to such a quantum critical point, Fermi liquid description breaks down and signs of "non-Fermi liquid" behavior appear. Signs for non-Fermi liquid properties are increased low energy excitations resulting in power laws when approaching lower temperatures as observed in the specific heat coefficient which is otherwise temperature independent in Fermi liquid, and in electric resistivity that displays exponents less than two. CeNi2Ge2 is one of the few heavy fermion compounds that shows these signs of non-Fermi liquid behavior without external pressure or chemical substitution. It has been suggested that non-Fermi liquid behavior is caused by quantum critical magnetic fluctuations close to an antiferromagnetic quantum critical point. In order to classify the nature of this non-Fermi liquid behavior, neutron scattering experiments were performed to find and characterize the relevant critical magnetic fluctuations. Several single crystals grown in collaboration with Leiden University and polycrystals grown in our lab have been studied. Beside the neutron scattering measurements performed on all available samples, we also carried out low temperature characterization measurements on part of these samples in dilution refrigerator and SQUID magnetometer. Electrical resistivity measurements have confirmed results reported by other researchers. Signs of non-Fermi liquid behavior below T=10K appear with the temperature dependence of electrical resistivity, DT~T^n, where