Which major poems by John Donne were published during his lifetime?

It is a common misconception that John Donne’s poetry was widely available during his lifetime; in fact, almost none of his poems were published while he was alive, as most circulated privately in manuscript copies among a small circle of admirers.1

The only important poetic works by John Donne published during his lifetime were the Anniversaries, which were released in 1611–1612. These poems, The First Anniversarie: An Anatomie of the World and The Second Anniversarie: Of the Progres of the Soule, were written to commemorate the death of Elizabeth Drury, the daughter of his patron, Sir Robert Drury.1

Most of his other famous works, including his Songs and Sonnets, "Holy Sonnets," and various elegies and satires, were not formally published until the posthumous editions of his Poems in 1633 and 1635.12