Causal structure discovery is a much-studied topic and a fundamental problem in Machine Learning. Causal inference is the process of recovering cause-effect relationships between the variables in a dataset. In general, causal inference problem is to decide whether X causes Y, Y causes X, or there exists an indirect relationship between X and Y via a confounder. Even under very stringent assumptions, causal structure discovery problems are challenging. Much work has been done on causal discovery methods with two variables in recent years. This thesis extends the bivariate case to the possibility of having at least one confounder between X and Y. Attempts have been made to extend the causal inference process to recover the structure of Bayesian networks from data. The contributions of this thesis include (a) extending causal discovery methods to the networks with exactly one confounder (third variable) ; (b) an algorithm to recover the causal graph between every pair of variables with the presence of a confounder in a large dataset; (c) employing a search algorithm to find the best Bayesian network structure that fits the data . Improved results have been achieved after the introduction of confounders in the bivariate causal graphs. Further attempts have been made to improve the Bayesian network scores for the network structures of some medium to large-sized networks using the standard ordering based search algorithms such as OBS and WINASOBS. Performance of the methods proposed have been tested on the benchmark datasets for cause-effect pairs and from the BLIP library.