The aim of this course is to introduce the interpolation polynomials of Lidstone, Whittaker, Schoenberg, Poritsky, Gontcharov, Macintyre and to give new applications of this theory to the question of integer valued entire functions of exponential type. The prerequisites are from complex analysis: Cauchy's residue Theorem, Cauchy's inequalities, series of analytic functions, Stirling formula. The course will include an introduction to Laplace transform.