Step 1: Identify the subject of the question.
The question asks for the author of the philosophical work titled 'Democracy and Education'.
Step 2: Recall or research the authorship of this specific book.
'Democracy and Education: An Introduction to the Philosophy of Education' is a seminal work in educational philosophy. It was published in 1916 by a prominent American philosopher, psychologist, and educational reformer.
Step 3: Evaluate the given options against this information.
(1) Russeau (Jean-Jacques Rousseau): A Genevan philosopher, writer, and composer. His influential work on education is 'Emile, or On Education'.
(2) Plato: An ancient Greek philosopher. His educational ideas are primarily found in 'The Republic'.
(3) John Dewey: John Dewey is widely recognized as the author of 'Democracy and Education'. His ideas significantly influenced progressive education.
(4) J. S. Mill (John Stuart Mill): An English philosopher, economist, and political theorist. His works include 'On Liberty' and 'Utilitarianism', but not 'Democracy and Education'.
Step 4: Conclude the correct author.
Based on the authorship, John Dewey is the author of the book 'Democracy and Education'.