This paper shows different multi-dimensional coordinate systems that can be applied on science and social sciences. This paper offers a serial of multi-dimensional coordinate systems to visualize and analyze from 4-Dimensions until Infinity dimensions into the same graphical space. At the inception of multi-dimensional coordinate systems, the following new types of multi-dimensional coordinate systems are presented: Pyramid coordinate system, Diamond coordinate system, 4-Dimensional coordinate system, 5-Dimensional coordinate system, Infinity Dimensional coordinate system and Multi-functional Pictorial coordinate system. These six Multi-Dimensional coordinate systems are constructed based on the traditional 3-D space concept, but they represent 4-D, 5-D, 8-D, 9-D and Infinity-Dimension