What are the types of coordinate system?

There are two main types: Cartesian coordinates and Polar coordinates.

In n-dimensional Cartesian coordinates there are n axes which are [usually] orthogonal and which meet at a single point called the origin. The coordinates of any point in the n-space are defined by the ordered n-tuple whose terms refer to the distances of the point, from the origin, along each of the axes.

In n-dimensional Polar coordinates, the point is located using its distance from the origin and the angles that this radial line makes with specified lines and planes.