I'm often interested in the history of Buddhist texts and, being a Theravadan, I'm not very familiar with the Mahayana texts. Please help to educate me in this manner.
The oldest existing manuscript clearly identified as Mahāyāna is a birch bark manuscript of the Aṣṭasāhasrikā-prajñāpāramitā-sutra or Discourse on Perfect Wisdom consisting of 8000 [Lines]. This manuscript was carbon dated to 47~147 CE. A version of this text was translated into Chinese in 179 CE by Lokakṣema and was amongst the first few Buddhist texts translated into Chinese.
However it's clear that some texts were being composed at quite an early period, perhaps as early as the 2nd Century BCE. One contender for the earliest Mahāyāna text is the Ugraparipṛccha, translated by Jan Nattier as A Few Good Men (2003). It shows a very early stage of Mahāyāna in which monks who dedicated themselves to meditation were known as bodhisatvas and lived alongside Mainstream monks.
Another serious contender is the Śālistamba Sūtra (translation published by N Ross Reat, 1993), which is clearly a little more developed than early Buddhist texts, but not yet a full-blown Mahāyāna text. It may well be considered a kind of "missing link" between the two phases of Buddhism. According to N. Ross Reat, the sutra could date as far back as 200 BCE.
Recently there were two very good articles on the very early Mahāyāna by David Drewes. See his academica.edu page "Early Indian Mahayana Buddhism" Parts I & II.
While there is no commonly recognized single oldest Mahayana sutra (see Wikipedia for general treatment of the topic), many scholars and practitioners believe some of the Prajnaparamita-series sutras to be very old.
Specifically, Aṣṭasāhasrikā Prajñāpāramitā Sūtra ("Perfection of Wisdom in 8,000 Lines") is believed to be written as early as 1st century BCE -- the earliest date I have personally seen anywhere for a Mahayana sutra. This sutra exists in two versions, one in verse and one in prose. As per Edward Conze, "for early Mahayana sutras that was quite a normal procedure."
The verse version is known as Prajnaparamita-Ratnagunasamcayagatha or simply "Ratnaguna". Based on linguistic analysis, Ratnaguna is thought to be the earlier of the two. According to Edward Conze, Ratnaguna's first 41 stances, known separately under the name of "Arya Prajna-Paramita Carya Gatha", are the earliest core. This makes Arya Prajna-Paramita Carya Gatha a good contender for a honorary title of the earliest Mahayana sutra.
It is available here as part of Edward Conze's complete translation of Ratnaguna and here translated by a committee under guidance of 16th Karmapa. Here I am posting my amateurish translation of the first 8 verses from BHS:
Super-loving-dear-grate-ful mood having established,
Having stopped sustaining the blinding emotions (avarana-klesha),
Listen carefully, oh the best of having gone forth
after Transcendental Wisdom, sages.
Any rivers flowing here in Jambu-dvipa (India)
Fruits-and-flowers, trees-and-grasses grow from which,
-- of the Mountain Dragon are running tears,
To his womb's grace this realm owes its existence.
Any Dharma declaring students of Victor,
Illuminating logically, cohesively, also elaborately,
And other people, fruit of happiness, through that work, attaining
-- of all these the producer is Tathagata.
What came from Victor, having spoken the guidebook of Dharma,
Following those instructions the best students acquire,
And from direct experience, as have seen, proclaim:
The state of Buddha is not a state of supermanly powers.
In it there is no acquisition of "Transcendental Wisdom" (Prajna-Paramita),
Also, no "Bodhisattva attainment", no "Enlightenment" of the mind.
-- This having heard but not confused nor panicking,
Bodhisattva engages in wisdom of the Lucky Ones (sugatas).
Also, not of body, nor feelings, nor thoughts, nor volitions,
Nor of consciousness, position even a little do not bother him.
Thus, to all dharmas not getting stuck, not getting caught into traps of abstractions (aniketacari)
Not clinging, he attains awakening of the Lucky Ones.
As venerable Shrenika the wandering beggar,
Understanding acquired, without precisely grasping the skandhas,
Just so bodhisattva, intuits real nature of things (dharmas).
And does not seek cessation (nirvritti) but abides in wisdom.
Having stopped again and again wavering searching for wisdom,
"Whence?", "Why?" -- of such dharmas empty,
Having stopped getting upset, caught up, or scared,
Soon he can reach awakening, such Bodhisattva.
That's quite a broad question, I certainly can't give it justice, but here are some starter points while we wait for better answers:
Mahayana Texts are preserved either via the Chinese Canon or the Tibetan Canon and certain of them were probably written outside of India.
These text were not memorized, these almost certainly were composed-- they are just too long to have been memorized.
They are in a completely different style-- attempting to imbue a sense of awe and wonder. I can't say it always works for me, some texts can get rather tedious in their "better than infinity plus one" exaggerations.
They tend to follow a pattern-- it starts out describing the Buddha getting ready to deliver a teaching, describes who is in attendance, and so on. The often include large sections about the merits of making copies of the sutras.
Thematically, I definitely don't have time to do them justice, they cover a lot of different themes. Some describe mantras and their benefits. Some describe Bodhisattva's-- their previous lives as monks and the various heroic vows they made. Some of them are philosophical discussions, sort of like Plato's dialogs.
The tantras sometimes get included in the broader category of Mahayana texts, but I haven't tried to read the tantras yet.
Keeping dependent arising in mind. The Gandharan Buddhist texts according to scholars contain samples of ancient Mahayana texts and teachings from the Dharmaguptaka school, the discovered texts have been dated to the 1st century CE. "Whose Buddhism in Truest?" an article written by Linda Heuman in Tricycle Magazine provides insightful information regarding these early texts and possible ramifications regarding the development of Buddhist traditions.