 Welcome to this NPTEL course on Introduction to Interfacial Waves. My name is Ratul Dasgupta. I am a faculty at the Department of Chemical Engineering at the IIT Bombay. Look at the collage of pictures on your right. You can see a variety of situations under which one encounters interfacial waves. Such waves are of interest as they appear in the natural world. They also appear in many situations which are commonly encountered in the industry. For example, in the natural world one encounters such interfacial waves through the oscillations of raindrops. These oscillations have influenced the measurement of the rate of rainfall. Such waves and the resultant spray that forms happens when waves break on the ocean surface. Such oscillations are also seen commonly when air blows over a body of water producing ripples and larger wavelength waves. In the industry such waves are also seen in the transport of heavy viscous oils using water as a lubricant. This is known as core annular flows and waves occur at the interface of the two. Such waves are seen in aluminum reduction cells. They appear as coating instabilities during coating of fibers. They also appear as bubble oscillations under ultrasound. We also see such waves as faraday waves during ultrasonic atomization which has applications in drug delivery. Through this course you will learn to analyze myriads of these situations. The structure of this course is designed to introduce you to the general area of vibrations and oscillations eventually leading to a deeper study of problems in hydrodynamic stability. The first part of this course will introduce you to problems of mechanical vibrations of systems which are simple and have finite number of degrees of freedom. The basic mathematical techniques for analyzing more complicated fluid mechanical situations will be introduced through analog examples of mechanical systems. The first part of the course will mostly deal with ordinary differential equations both linear and non-linear and various ways to solve them. In the second half of the course we will focus on interfacial waves and we will see what can we learn about interfacial waves by learning about mechanical oscillations of finite degree of freedom systems that we studied in the first half of the course. The course will prepare you to analyze most of these situations at the first order of approximation and beyond. It will also teach you to handle complicated flow situations like slug formation in gas liquid flows and spray formation in breaking waves. It will help you think about these things. This course will be of interest to students who are interested in understanding the fundamental principles of many area aspects of multiphase flows. It will also be of interest to practitioners in the field who are interested in many of these flow situations which are commonly appear in the industry. I hope to see all of you during the course.