This book is a translation of a substantially revised by F. Lösch edition of the world-famous reference book by E. Janke and F. Emde. It is a very special encyclopedia for special functions: it contains their definitions and many formulas, 73 tables and 210 original drawings and graphs of particular value. The tables provide sufficient accuracy for many applied issues and are convenient to use, and the drawings clearly illustrate the qualitative side of the behavior of functions.