The book is a self-contained comprehensive exposition of the equivariant degree theory and its applications to a variety of problems arising in physics, chemistry, biology and engineering. This monograph presents the theoretical foundations, construction, and the fundamental properties of the equivariant degree and its practical variations, which are applied to a series of examples from (functional) differential equations. It contains

a) the first thorough and complete introduction up to the present state of art to equivariant degree theory including non-abelian actions, and

b) provides for the first time several computer routines allowing an effective practical computation of the degree, illustrated by numerous concrete examples and charts.

The exposition of the material is mainly addressed to experienced researchers and graduate students interested in applications of equivariant topological methods, or working with differential equations and their applications, like physicists, biologists, chemists and engineers dealing with nonlinear dynamics with symmetries.