The book tells about the history of the emergence and key problems of modern quantum science, trying to penetrate the unimaginable depths of matter and find ways to other worlds, spaces and times. The wonders of the structure of the microcosm are discussed, in which the laws of everyday reality familiar to us cease to operate, and particles show "corpuscular dualism," becoming something between waves and particles, acquiring fantastic opportunities to penetrate barriers, form amazing pairs moving without electrical resistance, and generally "dissolve" in the environment, leaving behind only "bursts" of the electromagnetic field. The book is designed for the widest circle of readers interested in the successes of modern physics and scientific ideas about the structure of the surrounding quantum reality.