In the fast-paced technological revolution, technology has formed itself differently to facilitate the way to users to get their needs. As a matter of fact, people nowadays rely to a great extent on the smart devices as one of the essential creations of technology. They tend to access any website or web-application(s) through these devices fast and easily. Thus, paying enough attention to the design of any website or web-application is a major issue. This thesis project discusses the Responsive and Adaptive Design Methods as two important methods in terms of Websites and Web-Design. The methods have been theoretically discussed and explained to present the essential differences between them. Moreover, MyMusiC website has been implemented to show the differences between these methods practically. The prominent difference between the Responsive and Adaptive de-signs of the website makes it easy for the users to figure out the difference between the two design methods in terms of accessibility and ease of navigation. The results showed that the Responsive design is more user-friendly and more preferred by the users than the Adaptive design, as the users tend to use their smart devices first when they want to access a website than the computers.