This Master's Thesis is about, one of the most important tasks of microwave engineering: narrowband, and wideband impedance matching. The first part of the thesis introduces the fundamental quantities, and properties, used for impedance matching analysis. The following chapter presents, the basic construction of impedance matching networks, for pure real and complex terminations. The wideband techniques used in complex impedance matching cases are thoroughly presented. After the theoretical discussion of complex wideband impedance matching techniques, the most common analytic matching technique is presented, through a complete impedance matching task. In the second part of the thesis I discuss these impedance matching techniques, for use in electrically small, planar monopole antennas. The limitations of these common complex impedance matching techniques is presented (The Bode-Fano, and the Youla technique), through a design, and matching example of a planar Inverted L-Antenna. In the end, the results of the matching tasks, and further design development possibilities are presented.