ABSTRACT It is widely understood that superconductivity and magnetism are mutually exclusive or antagonistic due to their essentially different order states. But the recent discovery of the interplay between itinerant ferromagnetism and superconductivity in some uranium based compounds such as UGe2, URhGe, UCoGe, and UIrhas led to renewed interest in the relationship between ferromagnetism and superconductivity.Furthermore, there is also a wide range of interplay between superconductivity and magnetism in many non-uranium based compounds such as ZrZn2,Y9Co7, etc. The interplay of superconductivity and ferromagnetismis a long-standing and fascinating research problem in condensed matter physics. Even though the superconducting critical temperatureof UGe2, URhGe, UCoGe, and UIris low they are important for us to understand the physical origin of related properties of superconducting materials. In this Graduate Project Work, the superconductivity and itinerant ferromagnetism in ferromagnetic metalsUCoGe, UIr, and ZrZn2have been reviewed. Using the available data for UCoGe and UIr, phase diagrams of superconducting order parameter versus temperature, magnetization versus temperature, upper magnetic field versus temperature and density of state versus frequency have ben plotted and discussed for UCoGe and UIr. Key Words: Superconductivity, ferromagnetism, Curie temperature, UCoGe, UIr, ZrZn2