Greater India, also known as the Indian cultural sphere, or the Indic world, is an area composed of several countries and regions in South Asia, East Asia and Southeast Asia that were historically influenced by Indian culture, which itself formed from the various distinct indigenous cultures of South Asia. It is an umbrella term encompassing the Indian subcontinent and surrounding countries, which are culturally linked through a diverse cultural cline. These countries have been transformed to varying degrees by the acceptance and introduction of cultural and institutional elements from each other.

Since around 500 BCE, Asia's expanding land and maritime trade had resulted in prolonged socio-economic and cultural stimulation and diffusion of Buddhist and Hindu beliefs into the region's cosmology, in particular in Southeast Asia and the Far-East.

In Central Asia, the transmission of ideas was predominantly of a religious nature and short-lived, often co-existing with native philosophies such as Zoroastrianism and being quickly supplanted by the rise of Islam. In contrast, the spread of native Indian culture to East Asia was more multifaced and involved wide-ranging cultural exchange beyond religion.

By the early centuries of the common era, most of the principalities of Southeast Asia had effectively absorbed defining aspects of Indian culture, religion, and administration. The notion of divine god-kingship was introduced by the concept of Harihara, and Sanskrit and other Indian epigraphic systems were declared official, like those of the south Indian Pallava dynasty and Chalukya dynasty. These Indianized kingdoms, a term coined by George Cœdès in his work Histoire ancienne des états hindouisés d'Extrême-Orient, were characterized by resilience, political integrity, and administrative stability.

To the north, Indian religious ideas were assimilated into the cosmology of Himalayan peoples, most profoundly in Tibet and Bhutan, and merged with indigenous traditions. Buddhist monasticism extended into Afghanistan, Uzbekistan, and other parts of Central Asia, and Buddhist texts and ideas were accepted in China and Japan in the east. To the west, Indian culture converged with Greater Persia via the Hindu Kush and the Pamir Mountains.

The concept of the Three Indias was in common circulation in pre-industrial Europe. Greater India was the southern part of South Asia, Lesser India was the northern part of South Asia, and Middle India was the region near the Middle East. The Portuguese form (Portuguese: India Maior) was used at least since the mid-15th century. The term, which seems to have been used with variable precision, sometimes meant only the Indian subcontinent; Europeans used a variety of terms related to South Asia to designate the South Asian peninsula, including High India, Greater India, Exterior India and India aquosa.

However, in some accounts of European nautical voyages, Greater India (or India Major) extended from the Malabar Coast (present-day Kerala) to India extra Gangem (lit. "India, beyond the Ganges," but usually the East Indies, i.e. present-day Malay Archipelago) and India Minor, from Malabar to Sind. Farther India was sometimes used to cover all of modern Southeast Asia. Until the fourteenth century, India could also mean areas along the Red Sea, including Somalia, South Arabia, and Ethiopia (e.g., Diodorus of Sicily of the first century BC says that "the Nile rises in India" and Marco Polo of the fourteenth century says that "Lesser India ... contains ... Abash [Abyssinia]").

In late 19th-century geography, Greater India referred to a region that included: "(a) Himalaya, (b) Punjab, (c) Hindustan, (d) Burma, (e) Indo-China, (f) Sunda Islands, (g) Borneo, (h) Celebes, and (i) Philippines." German atlases distinguished Vorder-Indien (Anterior India) as the South Asian peninsula and Hinter-Indien as Southeast Asia.