 Professor G. K. Srinivasan from the Department of Mathematics at IIT Bombay and this will be a course on Fourier analysis and its applications. Despite its age, Fourier analysis continues to play a very significant role in modern research as well as large parts of pure and applied mathematics. The reason is very simple where there is harmony Fourier analysis makes its grand appearance. Its applications range from optics, wave propagation, geometry and number theory to name a few. In this course, the focus will be mainly on concepts rather than computations. Computational aspects will for the most part be relegated to exercises and problems. So, now let us take a brief look at the contents of this course. Some points of convergence will be addressed for Fourier series namely point wise convergence, mean convergence or the L2 theory, the Cesareau summability or Feier's theorem. As applications we shall give three applications, the classical problem in geometry called Dido's puzzle, a problem in celestial mechanics inverting of the Kepler equation and number theory, specifically Weyl's Equidistribution's theorem. These applications have been selected to demonstrate the wide applicability of Fourier analysis. We also see on the slide one of the main references, Elias Stein and Rami Shakarchi's book on Fourier analysis. This is the first volume of a four volume set which appeared about a decade ago and it's I think one of the finest modern introductions to Fourier analysis. We shall also go to the next section in the second part of the course on Fourier transforms and its applications to partial differential equations. We shall if time permits look at generalizations of Fourier series to more general sets of orthogonal polynomials and orthogonal functions. We shall supply nodes, problem sheets with partial solutions and hints to selected problems. We shall also give suggestions for further reading, suggest many projects, further research both in the field of pure and applied mathematics. Thank you.