Nāgārjuna (c. 150 – c. 250 CE) is widely considered one of the most important Buddhist philosophers. Along with his disciple Āryadeva, he is considered to be the founder of the Madhyamaka school of Mahāyāna Buddhism. Nāgārjuna is also credited with developing the philosophy of the Prajñāpāramitā sūtras and, in some sources, with having revealed these scriptures in the world, having recovered them from the nāgas (water spirits often depicted in the form of serpent-like humans). Furthermore, he is traditionally supposed to have written several treatises on rasayana as well as serving a term as the head of Nālandā.
Very little is reliably known of the life of Nāgārjuna, since the surviving accounts were written in Chinese and Tibetan centuries after his death. According to some accounts, Nāgārjuna was originally from South India. Some scholars believe that Nāgārjuna was an advisor to a king of the Satavahana dynasty. Archaeological evidence at Amarāvatī indicates that if this is true, the king may have been Yajña Śrī Śātakarṇi, who ruled between 167 and 196 CE. On the basis of this association, Nāgārjuna is conventionally placed at around 150–250 CE.
Some sources claim that in his later years, Nāgārjuna lived on the mountain of Śrīparvata near the city that would later be called Nāgārjunakoṇḍa ("Hill of Nāgārjuna"). The ruins of Nāgārjunakoṇḍa are located in Guntur district, Andhra Pradesh. The Caitika and Bahuśrutīya nikāyas are known to have had monasteries in Nāgārjunakoṇḍa. The archaeological finds at Nagarjunakonda have not resulted in any evidence that the site was associated with Nagarjuna. The name "Nagarjunakonda" dates from the medieval period, and the 3rd-4th century inscriptions found at the site make it clear that it was known as "Vijayapuri" in the ancient period.
There exist a number of influential texts attributed to Nāgārjuna though, as there are many pseudepigrapha attributed to him, lively controversy exists over which are his authentic works.
The Mūlamadhyamakakārikā is Nāgārjuna's best-known work. It is "not only a grand commentary on the Buddha's discourse to Kaccayana, the only discourse cited by name, but also a detailed and careful analysis of most of the important discourses included in the Nikayas and the agamas, especially those of the Atthakavagga of the Sutta-nipata.
Utilizing the Buddha's theory of "dependent arising" (pratitya-samutpada), Nagarjuna demonstrated the futility of [...] metaphysical speculations. His method of dealing with such metaphysics is referred to as "middle way" (madhyama pratipad). It is the middle way that avoided the substantialism of the Sarvastivadins as well as the nominalism of the Sautrantikas.
In the Mūlamadhyamakakārikā, "[A]ll experienced phenomena are empty (sunya). This did not mean that they are not experienced and, therefore, non-existent; only that they are devoid of a permanent and eternal substance (svabhava) because, like a dream, they are mere projections of human consciousness. Since these imaginary fictions are experienced, they are not mere names (prajnapti)."
According to David Seyfort Ruegg, the Madhyamakasastrastuti attributed to Candrakirti (c. 600 – c. 650) refers to eight texts by Nagarjuna:
the (Madhyamaka)karikas, the Yuktisastika, the Sunyatasaptati, the Vigrahavyavartani, the Vidala (i.e. Vaidalyasutra/Vaidalyaprakarana), the Ratnavali, the Sutrasamuccaya, and Samstutis (Hymns). This list covers not only much less than the grand total of works ascribed to Nagarjuna in the Chinese and Tibetan collections, but it does not even include all such works that Candrakirti has himself cited in his writings.
According to one view, that of Christian Lindtner, the works definitely written by Nāgārjuna are:
The Tibetan historian Buston considers the first six to be the main treatises of Nāgārjuna (this is called the "yukti corpus", rigs chogs), while according to Tāranātha only the first five are the works of Nāgārjuna. TRV Murti considers Ratnaavali, Pratitya Samutpaada Hridaya and Sutra Samuccaya to be works of Nāgārjuna as the first two are quoted profusely by Chandrakirti and the third by Shantideva.
In addition to works mentioned above, several others are attributed to Nāgārjuna. There is an ongoing, lively controversy over which of those works are authentic. Contemporary research suggest that some these works belong to a significantly later period, either to late 8th or early 9th century CE, and hence can not be authentic works of Nāgārjuna. Several works considered important in esoteric Buddhism are attributed to Nāgārjuna and his disciples by traditional historians like Tāranātha from 17th century Tibet. These historians try to account for chronological difficulties with various theories. For example, apropagation of later writings via mystical revelation. For a useful summary of this tradition, see Wedemeyer 2007.
According to Ruegg, "three collections of stanzas on the virtues of intelligence and moral conduct ascribed to Nagarjuna are extant in Tibetan translation": Prajñasatakaprakarana, Nitisastra-Jantuposanabindu and Niti-sastra-Prajñadanda.
Other works are extant only in Chinese, one of these is the Shih-erh-men-lun or 'Twelve-topic treatise' (*Dvadasanikaya or *Dvadasamukha-sastra); one of the three basic treatises of the Sanlun school (East Asian Madhyamaka).
Lindtner considers that the Mahāprajñāpāramitāupadeśa (Ta-chih-tu-lun, Taisho 1509, "Commentary on the great prajñaparamita") which has been influential in Chinese Buddhism, is not a genuine work of Nāgārjuna. This work is also only attested in a Chinese translation by Kumārajīva and is unknown in the Tibetan and Indian traditions. There is much discussion as to whether this is a work of Nāgārjuna, or someone else. Étienne Lamotte, who translated one third of the work into French, felt that it was the work of a North Indian bhikṣu of the Sarvāstivāda school who later became a convert to the Mahayana. The Chinese scholar-monk Yin Shun felt that it was the work of a South Indian and that Nāgārjuna was quite possibly the author. These two views are not necessarily in opposition and a South Indian Nāgārjuna could well have studied the northern Sarvāstivāda. Neither of the two felt that it was composed by Kumārajīva, which others have suggested.
From studying his writings, it is clear that Nāgārjuna was conversant with many of the Śrāvaka philosophies and with the Mahāyāna tradition. However, determining Nāgārjuna's affiliation with a specific nikāya is difficult, considering much of this material has been lost. If the most commonly accepted attribution of texts (that of Christian Lindtner) holds, then he was clearly a Māhayānist, but his philosophy holds assiduously to the Śrāvaka Tripiṭaka, and while he does make explicit references to Mahāyāna texts, he is always careful to stay within the parameters set out by the Śrāvaka canon.
Nāgārjuna may have arrived at his positions from a desire to achieve a consistent exegesis of the Buddha's doctrine as recorded in the āgamas. In the eyes of Nāgārjuna, the Buddha was not merely a forerunner, but the very founder of the Madhyamaka system. David Kalupahana sees Nāgārjuna as a successor to Moggaliputta-Tissa in being a champion of the middle-way and a reviver of the original philosophical ideals of the Buddha.
Nāgārjuna assumes a knowledge of the definitions of the sixteen categories as given in the Nyaya Sutras, the chief text of the Hindu Nyaya school, and wrote a treatise on the pramanas where he reduced the syllogism of five members into one of three. In the Vigrahavyavartani Karika, Nāgārjuna criticizes the Nyaya theory of pramanas (means of knowledge) 
Because of the high degree of similarity between Nāgārjuna's philosophy and Pyrrhonism, particularly the surviving works of Sextus Empiricus Thomas McEvilley suspects that Nāgārjuna was influenced by Greek Pyrrhonists texts imported into India. Pyrrho of Elis (c. 360-c. 270 BCE), who is usually credited with founding this school of skeptical philosophy, was himself influenced by Indian philosophy, when he traveled to India with Alexander the Great's army and studied with the gymnosophists.
Nāgārjuna's major thematic focus is the concept of śūnyatā (translated into English as "emptiness") which brings together other key Buddhist doctrines, particularly anātman "not-self" and pratītyasamutpāda "dependent origination", to refute the metaphysics of some of his contemporaries. For Nāgārjuna, as for the Buddha in the early texts, it is not merely sentient beings that are "selfless" or non-substantial; all phenomena (dhammas) are without any svabhāva, literally "own-being", "self-nature", or "inherent existence" and thus without any underlying essence. They are empty of being independently existent; thus the heterodox theories of svabhāva circulating at the time were refuted on the basis of the doctrines of early Buddhism. This is so because all things arise always dependently: not by their own power, but by depending on conditions leading to their coming into existence, as opposed to being.
Nāgārjuna means by real any entity which has a nature of its own (svabhāva), which is not produced by causes (akrtaka), which is not dependent on anything else (paratra nirapeksha).
sarvaṃ ca yujyate tasya śūnyatā yasya yujyate
sarvaṃ na yujyate tasya śūnyaṃ yasya na yujyate
All is possible when emptiness is possible.
Nothing is possible when emptiness is impossible.
As part of his analysis of the emptiness of phenomena in the Mūlamadhyamakakārikā, Nāgārjuna critiques svabhāva in several different concepts. He discusses the problems of positing any sort of inherent essence to causation, movement, change and personal identity. Nāgārjuna makes use of the Indian logical tool of the tetralemma to attack any essentialist conceptions. Nāgārjuna’s logical analysis is based on four basic propositions:
To say that all things are 'empty' is to deny any kind of ontological foundation, therefore Nāgārjuna's view is often seen as a kind of ontological anti-foundationalism or a metaphysical anti-realism.
Understanding the nature of the emptiness of phenomena is simply a means to an end, which is nirvana. Thus Nāgārjuna's philosophical project is ultimately a soteriological one meant to correct our everyday cognitive processes which mistakenly posits svabhāva on the flow of experience.
Some scholars such as Fyodor Shcherbatskoy and T.R.V. Murti held that Nāgārjuna was the inventor of the Shunyata doctrine, however, more recent work by scholars such as Choong Mun-keat, Yin Shun and Dhammajothi Thero has argued that Nāgārjuna was not an innovator by putting forth this theory, but that, in the words of Shi Huifeng, "the connection between emptiness and dependent origination is not an innovation or creation of Nāgārjuna."
Nāgārjuna was also instrumental in the development of the two truths doctrine, which claims that there are two levels of truth in Buddhist teaching, the ultimate truth (paramārtha satya) and the conventional or superficial truth (saṃvṛtisatya). The ultimate truth to Nāgārjuna is the truth that everything is empty of essence, this includes emptiness itself ('the emptiness of emptiness'). While some (Murti, 1955) have interpreted this by positing Nāgārjuna as a neo-Kantian and thus making ultimate truth a metaphysical noumenon or an "ineffable ultimate that transcends the capacities of discursive reason", others such as Mark Siderits and Jay L. Garfield have argued that Nāgārjuna's view is that "the ultimate truth is that there is no ultimate truth" (Siderits) and that Nāgārjuna is a "semantic anti-dualist" who posits that there are only conventional truths. Hence according to Garfield:
Suppose that we take a conventional entity, such as a table. We analyze it to demonstrate its emptiness, finding that there is no table apart from its parts […]. So we conclude that it is empty. But now let us analyze that emptiness […]. What do we find? Nothing at all but the table’s lack of inherent existence. […]. To see the table as empty […] is to see the table as conventional, as dependent.
In articulating this notion in the Mūlamadhyamakakārikā, Nāgārjuna drew on an early source in the Kaccānagotta Sutta, which distinguishes definitive meaning (nītārtha) from interpretable meaning (neyārtha):
By and large, Kaccayana, this world is supported by a polarity, that of existence and non-existence. But when one reads the origination of the world as it actually is with right discernment, "non-existence" with reference to the world does not occur to one. When one reads the cessation of the world as it actually is with right discernment, "existence" with reference to the world does not occur to one.
By and large, Kaccayana, this world is in bondage to attachments, clingings (sustenances), and biases. But one such as this does not get involved with or cling to these attachments, clingings, fixations of awareness, biases, or obsessions; nor is he resolved on "my self". He has no uncertainty or doubt that just stress, when arising, is arising; stress, when passing away, is passing away. In this, his knowledge is independent of others. It's to this extent, Kaccayana, that there is right view.
"Everything exists": That is one extreme. "Everything doesn't exist": That is a second extreme. Avoiding these two extremes, the Tathagata teaches the Dhamma via the middle...
The version linked to is the one found in the nikayas, and is slightly different from the one found in the Samyuktagama. Both contain the concept of teaching via the middle between the extremes of existence and non-existence. Nagarjuna does not make reference to "everything" when he quotes the agamic text in his Mūlamadhyamakakārikā.
Jay L. Garfield describes that Nāgārjuna approached causality from the four noble truths and dependent origination. Nāgārjuna distinguished two dependent origination views in a causal process, that which causes effects and that which causes conditions. This is predicated in the two truth doctrine, as conventional truth and ultimate truth held together, in which both are empty in existence. The distinction between effects and conditions is controversial. In Nāgārjuna's approach, cause means an event or state that has power to bring an effect. Conditions, refer to proliferating causes that bring a further event, state or process; without a metaphysical commitment to an occult connection between explaining and explanans. He argues nonexistent causes and various existing conditions. The argument draws from unreal causal power. Things conventional exist and are ultimately nonexistent to rest in the middle way in both causal existence and nonexistence as casual emptiness within the Mūlamadhyamakakārikā doctrine. Although seeming strange to Westerners, this is seen as an attack on a reified view of causality.
Nāgārjuna also taught the idea of relativity; in the Ratnāvalī, he gives the example that shortness exists only in relation to the idea of length. The determination of a thing or object is only possible in relation to other things or objects, especially by way of contrast. He held that the relationship between the ideas of "short" and "long" is not due to intrinsic nature (svabhāva). This idea is also found in the Pali Nikāyas and Chinese Āgamas, in which the idea of relativity is expressed similarly: "That which is the element of light ... is seen to exist on account of [in relation to] darkness; that which is the element of good is seen to exist on account of bad; that which is the element of space is seen to exist on account of form."
Nāgārjuna is often depicted in composite form comprising human and nāga characteristics. Often the nāga-aspect forms a canopy crowning and shielding his human head. The notion of the naga is found throughout Indian religious culture, and typically signifies an intelligent serpent or dragon, who is responsible for the rains, lakes and other bodies of water. In Buddhism, it is a synonym for a realised arhat, or wise person in general.