This book is devoted to the application of chiral-symmetric non-polynomial Lagrangians to the theory of mesons. In addition to an overview of the modern theory of quantized fields, the book provides original research by the authors, who own a number of results of fundamental significance. First of all, this concerns the development of new methods for constructing a theory for Lagrangians of a non-polynomial form, the theory of quantization of fields with spontaneously broken symmetry, as well as numerous physical applications that are of fundamental importance for the interpretation of experimental facts in the field of low-energy physics of mesons.