Ceva’s and Menelaus’ theorems are among the most important theorems in plane geometry. These theorems are very useful for establishing concurrency of lines and collinearity of points. In this graduate thesis it is show how these theorems can be generalized and proved in different ways. The thesis is divided into four chapters. In the first chapter, which contains auxiliary results, we explain barycentric coordinates of a point with respect to a given triangle. In the second chapter, Ceva’s and Menelaus’ theorems are proved in two different ways. The first proof is based on the area principle and the second one is via centroids. Afterwards, we show that the theorems are equivalent. In the rest of the thesis we generalize the main theorems in different ways and prove some of the generalizations in the plane and in space. In plane we study Hoehn’s theorem, Ceva’s and Menelaus’ theorems for polygons and one simultaneous generalization of both theorems. The final chapter is devoted to generalizations in space for space quadrilateral as well as Menelaus’ theorem in finite–dimensional vector spaces.