Lectures on orthogonal polynomials

These lecture notes contain a brief introduction to orthogonal polynomials and mention some applications which are not readily available in books on special functions and orthogonal polynomials. Since these lectures were prepared for a conference on differential equations and asymptotical theory in mathematical physics, we naturally emphasized differential equations satisfied by orthogonal polynomials and attempted to explain the role asymptotics play in the theory of orthogonal polynomials. Due to space and time limitations we have not treated orthogonal polynomials on the unit circle, nor have we touched the techniques of obtaining asymptotics of large zeros of special functions or largest and smallest zeros of orthogonal polynomials. The article by Rod Wong(65) in these proceedings complements this article and provides details of asymptotic techniques.