Regarding the Indian tradtion, Basham's is the classic work which covers the "Hindu" portion up to roughly 13th century, and excludes discussion of Islamic influence - which got covered by Vol 2 written by another scholar. I have just bought Vol 2, and is still awaiting the book to arrive in my mail box. In the mean time, some notes on texts mentioned: (more important ones in Bold)
Rg Veda - earliest surviving form of Sanskrit
Brahmanas - prose, e.g. Satapatha Brahmana
early Upanisands - religious significance
Yaska's Nirukta - oldest Indian linguistic text, dates from 5th century B.C.
Panini's Astadhyayi ("Eight Chapters") - composed towards the end of the 4th century B.C.
> Patanjali's Mahabhasya - 2nd century B.C.
> Kasika Vrtti of Jayaditya and Vamana - 7th century A.D.
Mahabharata - more important of the two Epics; includes Santi Parvan (Bhisma's sermon in his death), Bhagavad Gita, stories of Rama and Sita, Sakuntala, Savitri, Nala/Damayanti (longest narrative episode)
> Buddhacarita - 1st century A.D.
> fragment of plays
Bhasa: (author of 13 surviving plays, before Kalidasa)
> Svapnavasavadatta ("The Visions of Vasavadatta")
> Pratijnayaugandharayana ("Yaugandharayana's Vows")
> Abhijnanasakuntala ("The Recognition of Sakuntala") - play
> Vikramorvasi ("Urvasi Won by Valour") - play
> "Malavika and Agnimitra - play, comedy of harem intrigue
> Meghaduta ("Cloud-messenger")
> Rtusamhara ("Garland of the Seasons")
> Kumarasambhava ('The Birth of the War-god"
> Raghuvamsa ("Dynasty of Raghu") - incomplete
Sudraka's Mrcchakatika ("The Little Clay Cart") - play; probably contemporary of Kalidasa
Visakhadatta: (?6th century) - dramatist of politics
> Mudraraksasa ("The Minister's Signet Ring")
> Devicandragupta ("The Queen and Chandra Gupta") - in fragments only
Plays ascribed to Harsa:
> Nagananda ("The Joy of the Serpents")
Mahendravikramavarman's Mattavilasa ("The Sport of the Drunkards"): M is Pallava King; play is a farce
Pancatantra ("Five Treatises") - translated into Pahlavi in the 6th century
> Narayana's Hitopadesa ("Salutary Instruction") - composed in Bengal in 12th century, as reader for Sanskrit students
Dandin's Dasakumaracarita ("Tales of the Ten Princes") - prose, late 6th/early 7th century
Subandhu's Vasavadatta - good because of mastery of language, difficult to translate - late 6th/early 7th century
Bhavabhuti: (early 8th century, Kanyakubja; marks end of great Sanskrit dramatists; Indian critics regard him as second to Kalidasa)
> Malati and Madhava
> Mahaviracarita ("The Deeds of the Great Hero")
> Uttararamacarita ("The LAter Deeds of Rama")
Kumaradasa's Janaki-harana ("Rape of Sita")
Bharavi's Kiratarjuniya ("Arjuna and the Kirata")
Bhatti's Bhattikavya - 7th century, poem on the story of Rama
Magha's Sisupala-vadha ("Slaying of Sisupala") - 7th century
Sandhyakara's Ramacarita ("Deeds of Rama") - 12th century - allows for dual reading as story of Rama of Ayodhya or to the king Ramapala of Bengal - untranslatable
Bhartrhari's short poems - 7th century
Amaru's short poems - 7th century
> Harsacarita ("Deeds of Harsha") - 7th-century; gives fragment of autobography; apparently unfinished
> Kadambari - prose work, finshed by his son
Bilhana: (Kashmiri; 11th or 12th century)
> Caurapancasika ("Fifty Stanzas of the Thief")
Jayadeva's Gita Govinda ("Song of the Cowherd") - written in Bengal in the 12th century, still sung at the festivals of the Bengali Vaisnavite sects; rhymed
Somadeva's Ocean of Story - 11th century
Kalhana's Rajatarangini ("The River of Kings") - important for Kashmiri history
Nayacandra Suri's Hammira-mahakavya - Jaina monk, among the latest important works of Sanskrit literature
Other later dramatists:
Bhatta Narayana (?8th century)
Murari (early 9th century)
Rajasekhara (9th-10th centuries)
Krsnamisra (11th century)
Dandin's Kavyadarsa - 6th to 7th cenutry A.D.
Bhamaha's Kavyalamkara, 7th cenutry A.D.
Anandavardhana's Dhvanyaloka, 9th century A.D.
Mammata's Kavyaprakasa, early 12th century A.D.
Visvanatha's Sahityadarpana, 14th century A.D.