Ancient Indian philosophy says that man is the microcosm of the Universe. The Universe is referred to as the brahmanda (i.e. Egg of Brahma) and Man is referred to kshudra-brahmanda (i.e. Little Egg of Brahma). The Greeks also believed in the same concept (see wikipedia). The major points in favor of this correspondence are:
- The Divine who is Immanent in the World also situates a part of himself within every individual.
- There is a correlation between the seven planes of the Universe (Existence, Consciousness, Bliss, Knowledge, Mind, Vital, Physical) and the seven Chakras within Man.
- The three principles or Gunas (Sattwa, Rajas and Tamas) on which the Universe is formed also give rise to the transient personality (Prakriti) within Man.
- The Gods (i.e. cosmic energies) are said to be born twice according to the Rig Veda. They are born in the Universe as Cosmic Powers and they are also born in each individual when he or she experiences spiritual awakening.
- In both cases, evolution proceeds from the bottom to the top. In man, the Kundalini is awakened in the inconscient Muladhara Chakra and proceeds towards the Sahasrara Chakra at the top. Similarly, the Universe evolves from the Inconscient towards the Higher worlds. Essays in Philosophy and Yoga: Involution and Evolution
Within this earthen vessel are bowers and groves, and within it is the Creator.
Within this vessel are the seven oceans and the unnumbered stars.
The touchstone and the jewel-appraiser are within.
And within this vessel the Eternal soundeth, and the spring wells up.
Kabir says: “Listen to me, my Friend! My beloved Lord is within.”
Arthur Avalon on the correspondence as defined in Tantra
In this excerpt, John Woodroffe (Arthur Avalon) in his book Shakti and Shakta lays out how Tantra defines this microcosm-macrocosm relationship:
“It is necessary to remember the fundamental principle of the Tantra Sastra that man is a microcosm (kshudra-brahmanda). Whatever exists in the outer universe exists in him. All the Tattvas and the worlds are within him and so are the supreme Shiva-Shakti. The body may be divided into two main parts, namely the head and trunk on one hand, and the legs on the other. In man, the centre of the body is between these two, at the base of the spine where the legs begin. Supporting the trunk and throughout the whole body there is the spinal cord. This is the axis of the body, just as Mount Meru is the axis of the Earth. Hence man’& spine is called Meru-danda, the Meru or axis-staff. The legs and feet are gross matter which show less signs of consciousness than the trunk with its spinal white and grey matter, which trunk itself is greatly subordinate in this respect to the head containing the organ of mind, or physical brain, with its white and grey matter. The position of the white and grey matter in the head and spinal column respectively are reversed. The body and legs below the centre are the seven lower or nether worlds upheld by the sustaining Shaktis of the universe. From the centre upwards, consciousness more freely manifests through the spinal and cerebral centres. Here there are seven upper regions or lokas .. These regions, namely Bhuh, Bhuvah, Svah, Tapas, Jana, Mahah, and Satya Lokas correspond with the six centres; five in the trunk, the sixth in the lower cerebral centre; and the seventh in the upper Brain or Satyaloka, the abode of the supreme Shiva-Shakti” 
Sri Aurobindo on the correspondence in the Rig Veda
“This human ascension is possible because every being really holds in himself all that his outward vision perceives as if external to him. We have subjective faculties hidden in us which correspond to all the tiers and strata of the objective cosmic system and these form for us so many planes of our possible existence. This material life and our narrowly limited consciousness of the physical world are far from being the sole experience permitted to man, — be he a thousand times the Son of Earth. If maternal Earth bore him and retains him in her arms, yet is Heaven also one of his parents and has a claim on his being. It is open to him to become awake to profounder depths and higher heights within and such awakening is his intended progress. And as he mounts thus to higher and ever higher planes of himself, new worlds open to his life and his vision and become the field of his experience and the home of his spirit. He lives in contact and union with their powers and godheads and remoulds himself in their image. Each ascent is thus a new birth of the soul, and the Veda calls the worlds “births” as well as seats and dwelling-places.
For as the Gods have built the series of the cosmic worlds, even so they labour to build up the same series of ordered states and ascending degrees in man’s consciousness from the mortal condition to the crowning immortality… pure thought and feeling are man’s sky, his heaven; this whole vitalistic existence of emotion, passions, affections of which desire is the pivot, forms for him a mid-world; body and material living are his earth… he has to break through and out beyond these firmaments of earth and heaven; conquering firm possession of the solar worlds, entering on to his highest Height he has to learn how to dwell in the triple principle of Immortality.”
Sri Aurobindo, Hymns to the Mystic Fire: The Doctrine of the Mystics
Sri Aurobindo on the Higher-Lower division in Man and the Universe
“A separation, acute in practice though unreal in essence, divides the total being of man, the microcosm, as it divides also the world-being, the macrocosm. Both have a higher and a lower hemisphere, the parārdha and aparārdha of the ancient wisdom. The higher hemisphere is the perfect and eternal reign of the Spirit; for there it manifests without cessation or diminution its infinities, deploys the unconcealed glories of its illimitable existence, its illimitable consciousness and knowledge, its illimitable force and power, its illimitable beatitude. The lower hemisphere belongs equally to the Spirit; but here it is veiled, closely, thickly, by its inferior self-expression of limiting mind, confined life and dividing body. The Self in the lower hemisphere is shrouded in name and form; its consciousness is broken up by the division between the internal and external, the individual and universal; its vision and sense are turned outward; its force, limited by division of its consciousness, works in fetters; its knowledge, will, power, delight, divided by this division, limited by this limitation, are open to the experience of their contrary or perverse forms, to ignorance, weakness and suffering.”
Sri Aurobindo, The Synthesis of Yoga – I: The Ladder of Self-Transcendence
- John Woodroffe. Shakti and Shakta, p 133