At the end of the 20th century, it was discovered that the expansion of the Universe is speeding up. This acceleration is attributed to dark energy, which seems to be distributed uniformly almost everywhere and thus essentially influences the Hubble parameter H = H(t) characterising this expansion. In this book, the authors present current research in the study of the theory, implications and roles in cosmology of dark energy. Topics include gravitational aberration and the origin of dark energy; the role of dark energy in the evolution of the universe; the importance of supernova observations for exploring the nature of dark energy; and deformed quantum field theory, thermodynamics at low and high energies, and the dark energy problem.