Monitoring and control of the power system is based on static state estimation. With the invention advancement of technology of Phasor Measurement Units (PMUs), the concept of Wide Area Monitoring/Measurement Systems has been expanded as a key component of smart systems. Although the ability of PMUs in calculating the bus voltage and branch current synchrophasors allows continuous monitoring of power networks, high cost of these devices makes it necessary to find the minimum number and optimal placement of PMUs in order to achieve a desirable level of observability for solving the static state estimation problem so called Optimal PMU Placement (OPP) Problem. In this thesis, the fundamentals of PMU placement problem considering the limitations and possible contingencies is studied and a set of different optimization studies are conducted to consider various aspects of the problem. In this regard, algebraic and numerical observability analysis based on measurement matrix and topological observability based on network graph is achieved. Moreover, critical and redundant measurements are introduced and the impact of conventional measurements in OPP problem is discussed. In addition to introducing and solving the complete observability problem, the incomplete observability problem based on the concept of depth of unobservability is presented. Furthermore, partial observability and OPP problem as a multi-stage investment problem according to incomplete observability concept is presented. OPP problem is defined and investigated in the presence of single line contingency, loss of single measurement channel and single PMU Outage. Also, considering all the possible contingencies and constraints, a generalized OPP problem is defined which covers all of discussed conditions. Moreover, according to the fundamental principles of OPP problem for power system observability, the role of PMUs in fault location named fault location observability is investigated which has an important role in improving the power system reliability. Thus, the OPP problem is merged with fault location observability problem and the problem of PMU placement is presented not only with the aim of power system observability but also includes fault location observability. All of the defined optimization problems is evaluated on several test networks including IEEE 14-Bus, IEEE 30-Bus, 39 Bus New-England, and IEEE 57-Bus test networks. Keywords: 1-Phasor Measurement Units 2-Observability 3-Fault Location 4-OPP Problem