Natural products serve as a major resource for many pharmacologically-active drugs found in the market today. Using natural products as medicines, however, is associated with many limitations such as availability and isolation. An alternative to this is the synthesis of these compounds, which can be done using two different approaches: (1) Total synthesis of the molecule, and (2) A semi-synthetic approach. Total synthesis generally involves synthesis of the target molecule by assembling the ring systems or the core skeletal framework of the natural product. There are numerous methods reported in the literature for the synthesis of these ring systems. Despite this, there is always a quest for new methods; methods with improved efficiency in terms of chemo-, regio- and stereoselectivities. As a result, new synthetic tools are needed to address these issues. These new tools can be the development of new catalysts, new techniques, or innovative methodologies, which will allow new transformations and aid in the synthesis of complex natural products. In recent years small, strained molecules such as cyclopropanes, cyclobutanes and cyclopropenes, have been successfully employed for the synthesis of complex ring systems. In this dissertation a new method to access certain carbocyclic and heterocyclic ring systems using cyclopropanes as building blocks will be presented. This involves synthesis of novel cyclopropanes by intermolecular reaction between substituted styrenes and different alpha-arylmethyl-alpha-diazo compounds in the presence of Rhodium catalysts. The challenge in the synthesis of these cyclopropanes is that these diazo compounds are notorious for undergoing beta-hydride elimination reactions, thus limiting their use for intermolecular reactions. In this study, we aim to synthesize the proposed cyclopropanes in good yields while minimizing, if not completely eliminating, the beta-hydride elimination reaction. The first half of the thesis discusses the different approaches taken to synthesize the desired cyclopropanes with limited success. However using Rh2 (S-PTTL)3 TPA as the catalyst and optimizing the reaction conditions allowed us to synthesize these cyclopropanes in moderate to good yields. The second part of the thesis focuses on the study of ring opening reactions of the cyclopropanes synthesized using various Lewis acids.