This book aims to show the closed connection between approximation in respect of Hausdorff metric and analysis and synthesis of antenna grids. The second goal is to reveal how the tools of MATHEMATICA programming environment can be used in this direction. To this end series of MATHEMATICA codes illustrate numerical methods for finding optimal filters and antennas. The basic problems considered are approximation of functions and point sets by algebraic and trigonometric polynomials in Hausdorff metric as well as their applications in the field of antenna-feeder technique, analysis and synthesis of antenna patterns and filters, minimization of noise by suitable approximation of impulse functions. Fourier analysis is applied for approximation of impulse and transmitting functions and it is compared to the results obtained using the elements of the best Hausdorff approximation. The advantage of Hausdorff metric is the removal of the unpleasant effect of "Gibbs' phenomena". We hope that the book will be of interest for the researchers and specialists involved in analysis and synthesis of antenna patterns and filters facilitating their research.