Languages
Indian languages fall under two major and two minor families: the Indo-European languages (Indo-Aryan, 70%) and the Dravidian languages (22%), plus the Austro-Asiatic and Tibeto-Burman families and a few isolated languages.
The official language of the Union is Hindi, with English as an additional official language. The Constitution reads: "The official language of the Union shall be Hindi in Devanagari script." Interesting to note that the Constitution does not specify a national language at all. States have their own official languages: the southern state of Kerala has Malayalam, while Andhra Pradesh has Telugu.
Interesting quick fact: Malayalam, the language of Kerala, is a palindrome; it reads the same backwards.
There are several hundred languages spoken in various parts of the country. According to the 2011 census, India has 121 languages (22 official "Scheduled" languages and 99 others), grouped from over 19,500 raw mother-tongue responses - but only a much smaller number are spoken by most people. Here is a language map of India. See Wikipedia's full list of Indian languages.

Map: Language Map of India, CC BY-SA 4.0, via Wikimedia Commons.
| Language | Origins | Speakers* | Which region is it common in |
|---|---|---|---|
| Assamese/Axomiya | Indo-Aryan, Eastern | 13 | Assam |
| Bengali | Indo-Aryan, Eastern | 83 | West Bengal, Assam, Jharkhand, Tripura (list) |
| Bodo | Tibeto-Burman | 1.2 | Assam |
| Dogri | Indo-Aryan, Northern | 0.1 | Jammu and Kashmir |
| Gujarati | Indo-Aryan, Western | 46 | Gujarat, Maharashtra, Tamil Nadu (list) |
| Hindi | Indo-Aryan, various | 422 | the "Hindi belt", North India |
| Kannada | Dravidian, Southern | 38 | Karnataka, Maharashtra, Tamil Nadu, Goa (list) |
| Kashmiri | Dardic | 5.5 | Jammu and Kashmir |
| Konkani | Indo-Aryan, Southern | 2.5 | Konkan (Goa, Karnataka, Maharashtra, Kerala) |
| Maithili | Indo-Aryan, Eastern | 12 | Bihar |
| Malayalam | Dravidian, Southern | 33 | Kerala, Lakshadweep, Mahé, Puducherry |
| Manipuri (also Meitei or Meithei) | Tibeto-Burman | 1.5 | Manipur |
| Marathi | Indo-Aryan, Southern | 72 | Maharashtra, Karnataka, Madhya Pradesh, Gujarat, Andhra Pradesh, Goa (list) |
| Nepali | Indo-Aryan, Northern | 2.5 | Sikkim, West Bengal, Assam |
| Odia | Indo-Aryan, Eastern | 33 | Odisha |
| Punjabi | Indo-Aryan | 29 | Punjab, Chandigarh, Delhi, Haryana |
| Sanskrit | Indo-Aryan | 0.05 | Mattur |
| Santali | Austro-Asiatic, Munda | 6.5 | Santal tribals of the Chota Nagpur Plateau (comprising the states of Bihar, Chhattisgarh, Jharkhand, Odisha) |
| Sindhi | Indo-Aryan, Northwestern | 2.5 | Gujarat, Maharashtra, Rajasthan, Madhya Pradesh (list) |
| Tamil | Dravidian, Southern | 61 | Tamil Nadu, Karnataka, Puducherry, Andhra Pradesh, Kerala, Maharashtra (list) |
| Telugu | Dravidian, South-Central | 74 | Andhra Pradesh, Karnataka, Tamil Nadu, Maharashtra, Odisha (list) |
| Urdu | Indo-Aryan, Central | 52 | Jammu and Kashmir, Andhra Pradesh, Delhi, Bihar, Uttar Pradesh, Uttarakhand (list) |
* Speakers in Millions as per 2001 census
Most Indian languages have their own script. Here are details of Indic scripts