Until recently, the period of Late Antiquity had been largely regarded as a sterile age of irrationality and of decline in science. This pioneering work, supported by first-hand study of primary sources, argues that this opinion is profoundly mistaken. It focuses in particular on Proclus, the head of the Platonic School at Athens in the 5th c. AD, and the chief spokesman for the ideas of the dominant school of thought of that time, Neoplatonism. Part I, divided into two Sections, is an introductory guide to Proclus' philosophical and cosmological system, its general principles and its graded ordering of the states of existence. Part II concentrates on his physical theories on the Elements and the celestial bodies, in Sections A and B respectively, with chapters (or sub-sections) on topics including the structure, properties and motion of the Elements; light; space and matter; the composition and motion of the celestial bodies; and the order of planets. The picture that emerges from the study is that much of the Aristotelian physics, so prevalent in Classical Antiquity, was rejected. The concepts which were developed instead included the geometrization of matter, the four-Element composition of the universe, that of self-generated, free motion in space for the heavenly bodies, and that of immanent force or power. Furthermore, the desire to provide for a systematic unity in explanation, in science and philosophy, capable of comprehending the diversity of entities and phenomena, yielded the Neoplatonic notion that things are essentially modes or states of existence, which can be arranged in terms of a causal gradation and described accordingly. Proclus, above anyone else, applied it as a scientific method systematically. Consequently, that Proclus' physical thought is embedded in his Neoplatonic philosophy is not viewed as something regrettable, but as proof of his consistent adherence to the belief, that there must be unity in explanation, just as there is one in the universe, since only the existence of such unity renders the cosmos rational and makes certainty in science attainable.