Abstract
Cellular homology is a homology theory for CW complexes. Comparing to simplicial homology, cellular homology seems more abstract since its chain complexes are singular homology groups of CW complexes. In this thesis, we develop a combinatorial approach to rebuild cellular homology which does not rely on singular homology of CW complexes. Triangulability is a key assumption in this approach and it makes the treatment elementary and easy for computation. An isomorphism between combinatorial cellular homology and the original cellular homology based on singular homology will be established. The comparison between the two is discussed.