Recent discoveries in astronomy and relativistic astrophysics as well as experiments on particle and nuclear physics have blurred the traditional boundaries of physics. It is believed that at the birth of the Universe, a whirlwind of matter and antimatter, of quarks and exotic leptons, briefly appeared and merged into a sea of energy. The new phenomena and new states of matter in the Universe revealed the deep connection between quarks and the Cosmos. Motivated by these themes, this book discusses different topics: gravitational waves, dark matter, dark energy, exotic contents of compact stars, high-energy and gamma-ray astrophysics, heavy ion collisions and the formation of the quark - gluon plasma in the early Universe. The book presents some of the latest researches on these fascinating themes and is useful for experts and students in the field.