At their discovery in 2008, iron pnictide superconductors (IPS) provoked tremendous scientific interest, comparable to the discovery of the cuprate superconductors. So far, IPS reached critical temperatures T c up to 56K. Typically, they show an antiferromagnetic (afm) spin density wave (SDW) which has to be suppressed by doping before superconductivity develops, which then is supported by further doping. Due to the close vicinity of the magnetic and the superconducting (sc) phase, magnetic fluctuations are discussed to be responsible for the sc pairing mechanism in IPS. A special member of the IPS is LiFeAs, because it does not need doping to become sc. It is a stoichiometric superconductor at a T c of 18K. In fact, doping is suppressing its T c . Also, there is no sign of an afm SDW present. Therefore, LiFeAs is a interesting material to study the properties of the IPS in an undisturbed material. In 2010, experiments of the Leibniz Institute for Solid State and Materials Research Dresden (IFW Dresden) revealed further surprising properties of LiFeAs. Samples with a Li deficiency undergo a ferromagnetic (fm) phase transition at 165K. Theoretical calculations suggest that fm fluctuations could induce triplet superconductivity in LiFeAs. This would cause a nonvanishing dynamic susceptibility below T c , which is supported by nuclear magnetic resonance (NMR) experiments. This thesis is discussing the results of the IFW Dresden experiments, and concludes that this ferromagnetism is of weak itinerant nature. The origin might be an increase of the density of states (DOS) at the Fermi level, which is causing an instability towards fm order, as proposed by the Stoner model. For further doping experiments, the synthesis procedure of polycrystalline LiFeAs was optimized to get samples with maximum T c and minimum impurities. Therefore, nuclear quadrupole resonance (NQR) was used. The NQR line width is a measure of impurities in the sample. By minimizing the NQR line width, optimal samples were synthesized. These samples are able to compete with the properties of single crystals. To investigate the doping behavior of LiFeAs, a scenario with four different kinds of impurities and deficiencies was performed with the optimized synthesis procedure. 24 different samples were analyzed, by means of NQR and electrical conductivity. It was found that in fact Fe excess is responsible for changing the physical properties of LiFeAs, and not Li deficiency. It is causing a shrinking of the unit cell volume, as seen by X-ray diffraction (XRD) measurements and it causes a decrease of T c . It also leads to a decrease of room temperature resistivity, which is supporting an increase of the DOS at the Fermi level. The NQR frequency is scaling with the amount of Fe excess and can be used to draw the sc and fm phase diagram of off-stoichiometric LiFeAs. At an amount between 3.2 and 3.6% o f Fe excess LiFeAs undergoes the fm transition.