Remarkable advance in electronics science has occurred due to the significant progress in the electronic devices fabrication technology in Nano and Micro scales in recent years. Memristor is a new electronic component which was discovered by Leon Chua in 1971. Memristor can be fabricated in sub-micron dimensions. For the first time a practical prototype of memristor was fabricated by HP Company in 2008. Since then, it has drawn many research centers attentions from all over the world. Memristor memories provide non-volatile and high density solutions that can overcome some of the challenges faced by CMOS technology. Memristor memories use the memristor as a resistor with memory in which logics zero and one are represented by low and high resistances, respectively. Typically, the memristor's resistance range is divided in two halves, one state which falls in the lower half depicts logic zero and the other half shows logic one. In this thesis, first memristor is introduced and its electrical characteristics and applications in different areas are explained. Then the performances of different technologies in which memristor somehow are used are compared to each other. Then a detailed study of the non-linear model of the memristor is presented. The effect of some manufacturing parameters such as device length and material type on resistance ratio and also noise margin is studied. It is shown that when the ratio of the electrical conductivity doped region to that of the undoped region increases the resistance ratio of the device is improved regardless of the device length. After the formation of the conductive channel, the maximum resistance of the memristor i.e., ???????? will remain less than ????????. An equation explaining the relationship between ???????? and ???????? is given. The effect of the resistance ratio on writing and retention times of the memory formed by memristor is also studied. Keywords: Memristor, Nonlinear Element, Resistance Ratio, Writhing Time.