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Diluted magnetic semiconductors (DMS), semiconductors in which a fraction of non-magnetic sites have been replaced with their magnetic counterparts, have been in the limelight of the scientific community since the turn of the 21st century. The interest in these materials is spurred from their application in the spin electronics, the developing technology based on the usage of the fundamental property of every electron - its spin. Namely, diluted magnetic semiconductors have large spin-dependent properties that can be amplified in the presence of a magnetic field, thereby having the potential of achieving the external control of spin, which is the final goal of spintronics. The Achilles heel of diluted magnetic semiconductors is the material's quality. The tendency of magnetic ions distributed in a non-magnetic matrix is to cluster and form magnetic islands leaving non-magnetic regions in the material with macroscopic properties of the sample completely different from originally envisaged. The goal of this thesis was to develop novel synthesis methods to produce homogenously doped ZnO with transition metal ions (TM = Mn, Ni, Co) and to check what magnetic transition temperatures (Tc) could be achieved in such conditions. The idea was to use homogeneous precursors synthesized at low temperatures. A synthesis method was elaborated using transition metal doped nitrates as precursors. The materials were decomposed in moderately oxidizing conditions of NO2 formed during the synthesis. In the case of Mn as transition metal ion even this oxidation was strong enough to create a small quantity of Mn4+ and consequently, to form a small amount of parasitic magnetic phase ZnMnO3 within the Zn1-xMnxO matrix. Excellent material was produced by using a 2-step synthesis for DMSs based on inorganic precursor decomposition. The precursor was TM-doped hydrozincite, a zinc hydroxy carbonate salt, which is obtained by the oxidation of urea by Zn and Mn nitrates. This precursor undergoes a single-step decomposition to produce TM-doped ZnO at low temperatures. The detailed characterization of Mn-doped ZnO produced by this novel process demonstrates the high purity of its product. It is also compatible with Si-based device fabrication, because of the low-temperature nature of the process. In this case the formation of zinc manganate impurities was avoided as the oxidation state of Mn cations is well controlled. ZnO doped with up to 1.8 % of Mn has been prepared, and a ferromagnetic signal has been observed below 40 K. Unfortunately, this is well below the desired room temperature ferromagnetism. The goal is further on to increase TC with additional chemical manipulations. Other TM dopants in hydrozincite precursor did not give satisfactory results . The case of Zn1-xCoxO revealed that a strong ferromagnetism with TC > 260 K can be achieved when the Co precipitates in the ZnO matrix and hence it is not intrinsic to the system. The case of Zn1-xNixO has showed that NiO inclusions can lead to superparamagnetism. Besides chemical methods, a large variety of experimental techniques were employed to characterize the materials, such as X-ray diffraction (XRD), transmission electron microscopy (TEM), energy dispersive X-ray spectroscopy (EDXS), selected area diffraction pattern (SADP), electron energy loss spectroscopy (EELS), low and high-field electron spin resonance (ESR), DC and AC conductivity, AC susceptibility and Superconducting Quantum Interference Device (SQUID).