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This is a Printed Edition in B & W. After 'Records of the Future' and 'Aiming at REALITY', 'Nighing REALITY' is a step forward towards clutching the elusive notion of Reality. The InSight mission to Mars (book cover) is all about exploring the external world, with measurement being supreme: any instrument suspect of altering what it measures will be blamed on the incompetence of its designer -- not on Reality. Whether we make close contact with Reality or not will depend upon how cogently we process the data that the InSight explorer will transmit to us. With a philosophical introduction, followed by a conceptual presentation of Classical Physics, the evolution towards the new quantum paradigm is narrated through the discussion of spontaneous radioactivity, Ray and Wave Optics, Hamilton's mechanics, Einstein's light quanta, Bohr's atom, Quantum Entropy, and de Broglie's Wave Mechanics. The book ends with a conceptual presentation of how, motivated by persistent disagreement between theory and experiment, the first formulation of modern Quantum Physics -Matrix Mechanics- was born. In the process, the reader will understand that: 1. The relational behavior of a physical object vis