Subjects in English grammar are words, phrases, and clauses that perform the action of or act upon the verb.
Subject is a grammatical function.
Grammatical subjects should not be confused with semantic subjects, or the topic of the sentence.
Brinton, Laurel J. & Donna M. Brinton. 2010. The linguistic structure of Modern English, 2nd edn. Amsterdam: John Benjamins Publishing Company.
Hopper, Paul J. 1999. A short course in grammar. New York: W. W. Norton & Company.
Huddleston, Rodney. 1984. Introduction to the grammar of English. Cambridge: Cambridge University Press.