In this lecture, I will introduce adaptive clinical trial design and interim analysis procedures. The key issue is how to evaluate emerging evidence for efficacy or the lack of it thereof while maintaining the integrity, rigor and validity of the clinical trial. More specifically I will introduce a statistical procedure built on the concept of discordance probability, defined as the probability that the decision to reject or accept the null hypothesis based on interim data would be reversed should the trial continue to its planned end and be analyzed with a non-sequential test. At the trial design stage, this probability can be used to select an interim analysis procedure for a specific trial. In addition, once the interim analysis procedure is selected, we can evaluate the pre-trial discordance probability of the chosen procedure and document it in the protocol. I will demonstrate how rigorous advanced probability theory and statistical methods contribute to the establishment of the global clinical evaluation and drug development industry while discussing phase II and phase III trial design methods. I will discuss the implications of using the method in several cardiovascular and cancer clinical trials and ongoing emerging research in the field.