• Parivrajaka School: This school seeks to highlight the spiritual import of mantras. While several hymns of the Vedic Samhitas indeed convey spiritual ideas very directly, followers of this school of thought hold that even the other hymns can be explained in a spiritualistic manner. Examples of this method of interpretation are the commentary on the first 40 hymns by Shri Madhvacharya (13th cent. C.E.) and the commentary of Atmananda on the Asya Vamasya Sukta (Rigveda I.164). Kapali Shastri has written a spiritual commentary on the entire first Ashtaka of the Rigveda while Swami Brahmamuni has written a spiritual commentary on the entire Kauthuma Samaveda Samhita. This is not to say that this mode of interpretation is modern. Rather, the Brahmanas, Aranyakas and the Upanishads themselves expound numerous verses in the spiritual mode. In his Nirukta, Yaska cites the views of several followers of this method of interpretation, as does Sayana in his commentaries on various Vedic texts.
• Vaiyyakarana School: This is a general method of interpretation by the application of the rules of grammar to Vedic mantras. It is taken into account by all the other schools while commenting on the mantras. The Padapathas of the Vedic Samhitas is the earliest such commentary on these texts. These Padapathas seek to analyze the compound words occurring in the mantras according to certain rules of grammar. The Padapatha of Rigveda Samhita is by Shakalya, on Samaveda Samhita is by Gargya, and on the Taittiriya Samhita is by Atreya. The Padapathas on the Shaunakiya Atharvaveda Samhita, Maitrayani Samhita, Rigvediya Shankhayana Samhita, Rigvediya Ashvalayana Samhita, Shukla Yajurvediya Kanva Samhita and the Madhyandina Samhita also exist but are anonymous. Later grammarians however often reject a few analysis contained in the Padapatha as being opposed to the rules of grammar.
• Arya Samaj School of Interpretation: This was found by Swami Dayanand Sarasvati (1824-1883) and is exemplified by his commentary on the Madhyandina Yajurveda Samhita and approximately 7.5 mandalas of the Rigveda Samhita. After him, various scholars of the Arya Samaj have written numerous commentaries on the 4 major Vedic Samhitas in English, Hindi, Marathi and other Indian languages. These commentaries conform to the ideals regarding the Vedas propagated by the Arya Samaj: First, the Vedas are held to preach pure monotheism and therefore Agni, Indra etc., are held to be merely names of the one God. Second, the Vedas are said to encompass the Samhitas only, not the Brahmanas. Third, the Vedas are said to be the eternal word of God revealed at the beginning of creation, and as such, they are devoid completely of historical accounts or proper names. Fourth, since the Vedas are divine knowledge, they contain all the branches of knowledge (even modern ones like telegraphy, aeronautics and so on) in the root form. Fifth, all the modern commentaries on the Vedas are held to be spurious. Only the works composed by sages from Brahma to Jaimini (including the Brahmanas, Aranyakas, Sutras and so on) are held to reliable commentaries on the Vedas. Even these are to be rejected in so far as they are in conflict with the intent of the Samhitas. Sixth, even amongst the Samhitas, only the following 4 were revealed by God- Shakalya, Madhyandina, Shaunaka and Kauthuma. All the other Samhitas are composed by men and are like glosses on these 5 Samhitas. Seventh, the method of Yaska and Vyakarana are to be relied upon heavily to interpret the Vedas and the later Hindu texts like Puranas etc., must be rejected completely. There are several other principles followed by this school of interpretation (in one of his own works, Swami Dayanand himself lists 16 such principles).
• Shri Aurobindo’s School of Interpretation: This is a modern version of the ancient Parivrajaka school of interpretation and is discussed in numerous works of Sri Aurobindo like ‘The Secret of the Veda’ and of his followers like Kapali Shastri and David Frawley. Herein, the various gods in the Samhitas are said to represent different states of consciousness on the spiritual journey of men.
• Pauranic School: This is not really a school of interpretation, and refers to a few partial commentaries on the Vedic Samhitas that seek to discover the biographies of Hindu deities like Sri Rama and Sri Krishna in the hymns. This method is similar to the Aitihasika school, with the big difference that here that the ‘Itihasa’ does not pertain to the Seer of the hymn.
• Indological Method: This method is adopted currently by virtually all Vedic Scholars outside India and also by numerous scholars within India. It is has the greatest internal diversity and we have lumped various methods of interpretation of the Vedas only for the sake of convenience. Several members of this school take the Rigveda to be an Indo-European text that must be interpreted with the help of parallel traditions in the other branches of the Indo-European language family. Linguistics and Philology are relied upon heavily. Some Indologists like Ludwig suggested wholesale emendations in the traditionally handed texts, whereas others, like Max Mueller, strongly advocated the accuracy of the traditionally handed text. Scholars like Oldenberg completely rejected the traditional commentaries like those of Sayana, while others like Pischel emphasized that the Vedas are Indian texts and ought to be interpreted keeping in mind Indian paradigms as reflected in the traditional commentaries. Indologists of course take into account the Vedic Vyakarana, Nirukta and the Brahmanas and Kalpasutras into account, but are often also seen to reject their testimony on various grounds, some of which are highly conjectural. For instance, the AIT was taken as gospel truth in the past and accordingly a lot of hymns were interpreted as if they represented battles between tall, fair, long nosed Aryans and black, short native Indians. The most remarkable contributions of these scholars have been the creation of massive concordances, indices and scholarly exegetical notes on the Vedic texts (besides publishing critical editions of the same), correlation of ideas mentioned in the Vedic texts with parallel ideas in other literary traditions, analysis of the internal chronology of these texts and composition of exhaustive commentaries and translations in various languages. At times however, some of this work appears to be mere conjecture dressed up in jargon of the field, and too divorced from what the Vedic tradition has to say about itself. Nevertheless, an intensive study of both modern as well as old exegetical traditions is a must for comprehending the Vedic texts.
Polytheism, monotheism, monism have all been read into the Vedic hymns. Max Muller even coined the term “henotheism”, as the transitional stage between polytheism and monotheism in the hymns. It is the opinion of modern scholarship that the Vedic hymns reveal the gradual progress of philosophical thought i.e., from polytheism to monotheism to monism. This major flaw in interpretation is not surprising when it is understood that such an opinion springs from viewing Indian philosophy through a Western philosophical looking glass.