本书是函数领域的经典著作，适合对Schwarz 函数相关主题感兴趣的研究生和科研人员参考使用。H. A. Schwarz showed us how to extend the notion of reflection in straight lines and circles to reflection in an arbitrary analytic arc. Notable applications were made to the symmetry principle and to problems of analytic continuation. Reflection, in the hands of Schwarz, is an antianalytic mapping. By taking its complex conjugate, we arrive atan analytic function that we have called here the Schwarz Function of the analytic arc. This function is worthy of study in its ownright and this essay presents such a study. In dealing with certain familiar topics, the use of the Schwarz Function lends a point of view, a clarity and elegance, and a degree of generality which might otherwise be missing. It opens up a line of inquiry which has yielded numerous interesting things in complex variables; it illuminates some functional equations and a variety of iterations which interest the numerical analyst.