The work follows the ASPR and so is partly organized by manuscript.
First, we have the Junius Manuscript, with Genesis (A and B), Exodus, Daniel, Christ and Satan.
Then we have the Vercelli Book, with Andreas, The Fates of the Apostles, Soul and Body I, Homiletic Fragment I: On Human Deceit, The Dream of the Rood, Elene.
This is followed by the Exeter Book, which, being devoted to poetry in particular, has a fair number of different poems of different kinds, the most famous of which are probably The Wanderer and The Seafarer.
After this we have Beowulf and Judith, which are the poetic works found in the Nowell Codex.
Then comes the Paris Psalter, which, being a metrical translation from Latin, is paired with the poetry from translations of Boethius's Consolation of Philosophy.
Then there are a lot of minor poems, of which the most famous are probably The Battle of Maldon and Bede's Death Song.
And last there are the additional poems not included in the ASPR.
Tom Shippey in his introduction to the book makes an excellent comment on the whole corpus, which will do well enough to start us off:
The poems we have are also, in their way, almost all "last survivors": only three of them, apart from the Chronicle poems and the poems ascribed to Caedmon and Bede, and found in many manuscripts, duplicate each other. Some of the poems are, furthermore, fragments, including the Maldon and Finnsburg poems and Judith. As for the corpus itself, it is now a ruin. Certainly it exists. But its existence is at least a reminder of what no longer exists, a whole tradition of which we can hear only, here and there, murmurs and echoes....The poems exist, often in fragmentary form, and like the old ruins, they bear testimony to all that they remember, even if it has vanished. (p. l)