The time before the War of Wrath and the expulsion of Morgoth from the world; the First Age long predated the first rising of the Sun, but after this point years can be numbered from I 1
The first of the four Ages chronicled by Tolkien. Unlike the Second and Third Ages, there is no detailed chronicle of the events of the First Age, at least in any canonical sources, and so some dates must be inferred from references in the text - hence many dates in this Age are necessarily approximate. We do have two sources for dating this period, The Annals of Aman and The Grey Annals, in volumes X and XI of The History of Middle-earth respectively. While not formally canonical, in the absence of any other comparable material, these sources are especially useful in dating events of the First Age. This entry deals with events of the First Age of the Years of the Sun; for earlier events see the entry for Years of the Trees, and for the rationale behind this distinction, see the essay Dating the First Age below.
Expulsion of Morgoth from the world; end of the First Age
For a full chronicle of events from the First Age, see the Chronicle of Arda
Dating the First Age
Establishing the point where the First Age began is not as simple as might be imagined. The only really definite statements are in the drafts of the Appendices to The Lord of the Rings, which originally included this comment, relating to the time of the awakening of the Elves:
The History of Middle-earth volume XI, 3 V The Tale of Years
According to this dating, the First Age began about 4,312 years before the rising of the Sun, making the entire Age some 4,902 years long. This calculation is backed up by a further comment from other drafts of the Appendices:
'The First Age was the longest.'
The History of Middle-earth volume XII, 1 VI The Tale of Years of the Second Age
It's perhaps notable that no direct comment on the beginning of the First Age, or its length, survived into the published version of the Tale of Years (which indeed does not attempt to provide a chronicle of the First Age at all). It's hard to be sure why this should be, but part of the problem was doubtless the complication of having two dating systems: one before the rising of the Sun, and one after.
The whole notion of measuring time in 'years' is of course dependent on the existence of the Sun, so before it was created, a different dating system was needed. This worked on so-called 'Valian Years', dating from the making of the Two Trees; on this system the first Elves awoke in 1050. However, Valian Years were rather longer than solar years, so 1050 is equivalent to about 10,062 conventional years (actually there are various ways of making this calculation, so this is necessarily an approximation). We might imagine that the beginning of the First Age would restart the count of years, but in fact that did not happen until the Sun was created 1500 Valian Years (about 14,374 solar years) after the making of the Trees. From that point the First Age is dated in normal years.
So, a full chronicle of the First Age would involve two dating systems, using two different types of years; first a period of 450 Valian Years (4,312 solar years) starting in (Valian Year) 1050, then a period of 590 solar years starting at year 1 (the rising of the Sun).
Dates using the former system fall within the period known as the Years of the Trees (where they are used in entries here, they are given in Valian Years, usually with a suitable conversion to solar years). Dates after the rising of the Sun began a new sequence known as the Years of the Sun (sometimes abbreviated to 'YS').1
To keep dates consistent in form, these Years of the Sun in the First Age - from the first rising of the Sun to the end of the Age - are here given the prefix 'I' (followed by 'II' for the Second Age, 'III' for the Third Age, and so on). Thus the year 'I 1' refers to the appearance of the Moon and Sun, and to the Awakening of Men. By most definitions it was not the actual first year of the First Age, but it was the first measurable Year of the Sun in that Age.
Notes
1
These solar years are used by Tolkien himself, for example, in the Grey Annals and various associated genealogies published in volume XI of The History of Middle-earth. The Grey Annals describe events both before and after the rising of the Sun, so they necessarily include the changeover from one dating system to the other. In that source, the first year of the new system is labelled 'YS 1', and thereafter no further prefix is used (since these annals never extend beyond the First Age, there is no risk of confusion with later Ages).