Various types of polygons have been shown in this graduate thesis and some of their properties have been proven. Triangles are classified in two general ways: by their sides and by their angles. On the basis of that, we can notice some of the characteristic properties of the triangles. There are also some lesser-known types of triangles such as the pseudo right triangle that is characterized by a certain relation between the angles of the triangle. Some types of triangles are defined by another triangle, such as the pedal triangle whose vertices are equal to foots of the lines perpendicular to lines that contain sides of the given triangle, passing through a given point. When that point fits with the orthocenter of the given triangle, then the resulting triangle is called orthic, and if this point is the center of the circumcircle, the triangle is called medial. There is a triangle which is called perfect whose perimeter and area are equal and the lengths of its sides are natural numbers. Also, there is the gold triangle which is defined by the golden ratio. Likewise, we find the golden ratio in the regular or gold pentagon. In this paper various types of quadrilaterals were observed. In addition to well-known types of parallelograms, there are quadrilaterals that have the circumcircle or the incircle, and we call them cyclic and tangential quadrilaterals respectively. A special kind of tangential quadrilateral is the one with perpendicular diagonals and is called deltoid. Furthermore, some polygons with five and more sides have been researched, such as Pascal and Brianchon hexagon.