The book is a reference and user manual for the latest systems of symbolic (analytical) mathematics - Maple 9.5 and Maple 10. These are recognized world leaders in the field of analytical computing that have passed serious certification in this area. The interface of systems and their extensive capabilities in mathematics, physics and education are briefly described. Particular attention is paid to the technique of practical calculations and visualization of their results, as well as the solution of differential equations of various types. Described are means of symbolic and numerical calculations, graphic and software capabilities of systems, packages of their extension, maplets and practice of using Maple in mathematical and physical calculations.