Eliot's poetry book for children about cats.
Eliot wrote the poems in the 1930s and included them, under his assumed name "Old Possum", in letters to his godchildren. 

Old Possum’s Book of Practical Cats was published on 5th October 1939 in an edition of 3005 copies with cover illustrations by TS Eliot. This first edition, however, lacked illustrations inside the book and so Nicholas Bentley was commissioned to illustrate a new edition in 1940.

For offer are both books:

Old Possum’s Book of Practical Cats
London: Faber & Faber Limited. 
FIRST UK EDITION. 1st Edition. 1st Printing. 1939.
Dust wrapper is price clipped, otherwise, no tears. 
Near Fine Hardcover yellow cloth binding.  
Minimal to no foxing to the front free end paper otherwise very clean and presentable with no previous owner’s ink.
The inscription is Eliot’s own and reads, “To One From One. Christmas 1939.”

Old Possum’s Book of Practical Cats Illustrated by Nicholas Bentley.
London: Faber & Faber Limited. 
SECOND IMPRESSION, first illustrated edition November MCMXL (1940). 
Dust wrapper is price clipped. Torn at top and bottom of spine.
Very Good Hardcover cream cloth binding.  
Owner’s Book Plate pasted on inside end paper.
Minimal to no foxing to the front free end paper otherwise very clean and presentable with no previous owner’s ink.

Both books come in a custom bookbinding box.

From a smoke free home.