Since the discovery three decades ago, fullerenes as well as metallofullerenes have been extensively investigated. However, almost all known fullerenes follow the classical definition, that is, classic fullerenes are comprised of only pentagons and hexagons. Nowadays, more and more evidence, from both theoretical and experimental studies, suggests that non-classical fullerenes, especially heptagon-containing fullerenes, are important as intermediates in fullerene formation mechanisms. To obtain fundamental understandings of fullerenes and their formation mechanisms, new systematic studies should be undertaken. Although necessary tools, such as isomer generating programs, have been developed for classical fullerenes, none of them are able to solve problems related to non-classical fullerenes. In this thesis, existing theories and algorithms of classical fullerenes are generalized to accommodate non-classical fullerenes. A new program based on these generalized principles is provided for generating non-classical isomers. Along with this program, other tools are also attached for accelerating future investigations of non-classical fullerenes. In addition, research to date is also reviewed. / Master of Science / The thesis describes the generation of heptagon-containing fullerene structures based on generalized spiral algorithm. Details of algorithms and designs are discussed. The thesis is helpful for people who are working on fullerene geometry studies. The algorithms and programs provided by this thesis could be a good start for other investigations. For those who are not familiar with programming, the program provided by this thesis can also be used to generate and analyze heptagon-containing structures. In addition, this thesis can also be helpful for people working on areas that geometry analyses of molecules are necessary.