 Hello students, welcome to the course on Modeling Stochastic Phenomena for Engineering Applications. I am Dr. Y. S. Maya, Visiting Faculty in the Department of Chemical Engineering at IIT Bombay. I was teaching this course to research scientists at the Bhabha Atomic Research Centre till my retirement in 2012. Since then, I have been offering this course at IIT Bombay. Stochastic processes refer to phenomena which have inbuilt randomness and consequent unpredictability in their occurrence. These phenomena should be contrasted with deterministic processes. Processes which are described by mechanistic laws such as Newton's laws of motion. In deterministic systems, once initial conditions are specified, it is possible to predict their future states precisely through the mechanistic laws. Planetary motion is a well known example of a deterministic system. On the other hand, in stochastic systems, persistent random fluctuations make it impossible to carry out precise predictions of future outcomes. One can only describe them with the probability distributions. The motion of an air parcel in the atmosphere or the rise and fall of prices of commodities or the transfer of infections across populations are some of the examples of stochastic processes. Broadly speaking, stochastic description is a part of statistical science. However, there is a subtle difference between classical statistics and stochastic modelling. Classical statistics deals with the probabilities of outcomes of random experiments without taking into account the temporal sequences or temporal relationships between the various outcomes. One example is the tossing of a fair coin, let us say n times. The outcomes of heads or tails or their distributions do not depend upon the order in which different tosses are indexed. This belongs to classical statistics. In contrast, stochastic modelling explicitly deals with the time-ordered processes. It deals with how a system subject to random fluctuations evolves in time. The distinction between the present and the future is at the heart of stochastic modelling. A classic example of a stochastic process is what is known as Brownian motion of small particles suspended in liquids or gases. Although particles are far more massive than the molecules of the fluid, they experience a macroscopically visible random motion due to constant bombardment from the molecules. As a result, a new probabilistic law emerges for the motion of particles when we examine it through the stochastic perspective. In view of its fundamental significance, we study Brownian motion in considerable detail throughout this course. To sum up, this course is a foundational exposition of evolution of systems subject to random fluctuations. We proceed to explore this evolution through three different approaches. We start with what is known as a Markovian random walk approach, basically for discrete jumping processes. Then we pass over to a differential equation description known as the Fokker Planck equation. We also touch upon briefly with what is known as Langevin dynamics approach. Finally, we study stochastic phenomena through master equation approach which is often used in chemical kinetics. Throughout, we develop the necessary mathematical and statistical tools such as central limit theorem and Markovian assumption. These examples will be discussed to illustrate the models as we go along. The basic requirement for the course is undergraduate third or fourth year engineering level or master's in physics level. The student is assumed to be familiar with the introductory knowledge of differential and integral calculus, differential equations, infinite series, elementary mathematical functions, rudiments of Fourier and Laplace transforms, elementary statistics and concepts of probability distributions. I presume the course will be useful for those pursuing physics, chemical and mechanical engineering, data science, signal processing and several other physical sciences. Although we restrict ourselves to engineering perspectives, the course will be helpful to those pursuing mathematical modeling in environmental and climate sciences, in behavioral sciences, in economics and potentially a host of other social sciences as well. We will go along by systematically deriving various mathematical formulations and their solutions. I once again welcome you to this course and wish you a pleasurable learning experience. Thank you.