In this thesis a parametric study of various broadband microstrip patch antennas and a dual band patch antenna is investigated. The broadband patch antennas studied in this thesis are: a rectangular microstrip patch antenna with a U-shaped slot, a rectangular microstrip patch antenna with a circular arc slot, a circular patch antenna with a circular arc slot and a circular patch antenna with a circular arc slot and L-shaped probe. The feed for these antennas is a coaxial probe feed. Different parameters such as probe radius, probe location, substrate height, width of the slot and location of the slot are considered in the parametric study. The resonance behavior of a rectangular patch a tenna with a U-slot and a rectangular patch antenna with a circular arc slot is also investigated. The radiation patterns, gain patterns and the return loss of the broadband antennas are also discussed. For dual band operation, a new coaxially-fed microstrip patch antenna with two asymmetric U-shaped slots is discussed in this thesis. Two approximate equations for the resonant frequencies based on the surface current distribution are presented. The simulation results of the radiation patterns, gain patterns and the return loss of the antenna are presented. In addition, a single U-slot patch antenna, a rectangular microstrip patch antenna with a circular arc slot, and dual U-slots patch antenna are fabricated and tested in the Antenna Laboratory at the University of Manitoba. The simulation and experimental results are then compared.