Abstarct: The location problems that are one of the most practical problems in operations research, are defined as follows; Finding a set of service providers, so that total service costs to the customers are minimum compared to a set of constraints. In other words, in these problems we are finding optimal location and how to place one or more service providers baxsed on effective factors and variables on the location. First we investigate different models of classical location problems include multi facility location problem, p-median, p-center, and un capacitated facility location problem. One of the other location problems is inverse location problems. In an inverse location problem, some of the input parameters of system, such as weight of vertices or length of edges are changed by the cheapest or the most profitable method in order to optimize pre-arranged facilities, under the new parameters. So we investigate models of location problems with budget constraint and minimum cost and p-median inverse location problem. Another branch of location problems is line location problems wherein instead of finding a point, we are locating a line. In fact, the aim is finding a straight line in the plane or space, so that sum of the weight intervals or maximum of given points’ weight intervals to the desired line is minimum. we present the location problems of line median and line center, then we will investigate different types of line location and related models such as limited line location, line location with positive and negative weights by Euclidean and rectangular norms. And the last category of location problems investigated in this thesis, is the inverse line location problems wherein we consider a feasible line and the aim is changing the problem parameters in order to minimum the costs and convert the given line to an optimal one. These changes can be created in weight of vertices or coordinates of points or both of them. we present six different models of inverse line location problems include inverse line location problem with minimum cost by changing the weight of vertices, coordinate of points, or both of them under Euclidean and rectangular norms, also inverse line location problem with budget constraint by changing the weight of vertices, coordinates of points, or the both under Euclidean and rectangular norms.