What powerful thoughts and feelings are conveyed in the William Butler Yeats' poem "The Lake Isle of Innisfree?"

Yearning for peace in the company of nature is the most powerful thought in the poem.

The poet is a man of city. What troubles him in the city is not specified. However, it’s understood that the poet wants to escape from the drab urban setting to a pristine world of nature.

The poem takes up the common Romantic theme of return to nature. The period around 1888, when this poem was composed, saw rapid industrialization and urbanization all over England and Europe. It resulted in man's distancing away from the idyllic natural world.

The poet desires to transcend all the worries that saddle and depress him in the city. Nature seems to be the only refuge that could guarantee him the solace he’s seeking.

And I shall have some peace there, for peace comes dropping slow,
Dropping from the veils of the morning to where the cricket sings;
There midnight’s all a glimmer, and noon a purple glow,
And evening full of the linnet’s wings.

For the upsetting urban environment, the poet turns to Innisfree, a small island at Lough Gill in Sligo County. It had been Yeats’ childhood haven. He would frequently visit the place with his family and enjoy a lot.

So, we see nostalgia is another significant feeling expressed in the poem. Innisfree is a symbol for perfect idyllic setting, where the poet is sure to discover internal peace.

Besides, the strong dislike for modern settlement is another very important feeling expressed in the poem. The description of his imagined cabin suggests his distaste for modern lifestyle.

And a small cabin build there, of clay and wattles made;

The cabin that he would set up would be made of "clay and wattles," both of which are naturally available. There’s no mention of anything that’s factory-made.

The only image borrowed from the city is that of “roadway” and “pavements,” and interestingly, they look “grey.” The choice of color speaks amply about the poet’s opinion about urban lifestyle.

So, we see that the poet wants to run away from the stifling city life and seclude himself in the soothing world of nature.