The Tipitaka (Pali ti, "three," + pitaka, "baskets"), or Pali canon, is the collection of primary Pali language texts which form the doctrinal foundation of Theravada Buddhism. The Tipitaka and the paracanonical Pali texts (commentaries, chronicles, etc.) together constitute the complete body of classical Theravada texts.
The Pali canon is a vast body of literature: in English translation the texts add up to thousands of printed pages. Most (but not all) of the Canon has already been published in English over the years. Although only a small fraction of these texts are available on this website, this collection can be a good place to start.
The Digha Nikaya, or "Collection of Long Discourses" (Pali digha = "long") is the first division of the Sutta Pitaka, and consists of thirty-four suttas, grouped into three vaggas, or divisions:
Silakkhandha-vagga — The Division Concerning Morality (13 suttas)
Maha-vagga — The Large Division (10 suttas)
Patika-vagga — The Patika Division (11 suttas)
An excellent modern translation of the complete Digha Nikaya is Maurice Walshe's The Long Discourses of the Buddha: A Translation of the Digha Nikaya (formerly titled: Thus Have I Heard) (Boston: Wisdom Publications, 1987). A fine anthology of selected suttas is Handful of Leaves (Vol. 1), by Thanissaro Bhikkhu (distributed by the PTS).
The translator appears in the square brackets []. The braces {} contain the volume and starting page number in the PTS romanized Pali edition.