In this thesis we address the problem of leaning Markov network structure from data by presenting the Dynamic GSIMN or DGSIMN algorithm. DGSIMN is an extension of GSIMN algorithm, and works by conducting a series of statistical conditional independence tests on the data, and uses the axioms that govern the independence relation to avoid unnecessary tests i.e., tests that can be inferred from the results of known ones. However, DGSIMN improves on the GSIMN algorithm by dynamically selecting the locally optimal test that will increase the state of knowledge about the structure the most. This is done by estimating the number of inferences that will be obtained after executing a test (before it is actually evaluated on data), and selecting the one that is expected to maximize the number of such inferences. This helps decreasing the number of tests required to be evaluated on data, resulting in an overall decrease in the computational requirements of the algorithm. Experiments show that DGSIMN yields savings of up to 85% while achieving similar or better accuracy in most cases.