A cell complex is a means of taking a complicated shape or system, and breaking it into simple pieces called cells. Thus, a cell complex is a set of cells that ``fit together in a nice way.'' Recall that one of our goals is to provide a means of understanding complicated systems in terms of a set of interacting simpler pieces. This is the role of the cell complex - a cell complex can be used to represent a complicated system that has been partitioned into simpler pieces (the cells). The properties of a cell complex are used to guarantee that regions of interaction among the simple parts of the system (the cells of the complex) are represented by (lower dimensional) cells contained in the complex.