This lecture describes the approach the authors of the color space representation and use them for color image processing. This leads into the formulation of the color space as three-dimensional vector space, with all related structures. However, after defining the essential elements of the vector space are identified, can be extended to other color space, perhaps for different creatures and devices, and other dimensions than three. CIE space is presented as a prime example of color space. Having established the vector space formulation, decomposition of the various benefits of space can be built. This leads to direct decomposition-total color space where the two-dimensional subspace to identify the attributes of color, and the third coordinate to provide lighting. Finally, see how the three types of color deficiency is present in some groups of people to cause decomposition of the direct-sum of three one-dimensional subspaces associated with three types of cone photoreceptors in human retina.