Classical archaeology is the archaeological investigation of the Mediterranean civilizations of Ancient Greece and Ancient Rome. Nineteenth-century archaeologists such as Heinrich Schliemann were drawn to study the societies they had read about in Latin and Greek texts.
Historical archaeologists certainly make use of written records, but not all research that involves written records is classified as “historical archaeology”. For example, the writings of Meso-American cultures are studied by archaeologists, but their work is not generally considered to be “historical archaeology”.
Archaeology is the study of cultures that lived in the past. It is a subfield of anthropology, the study of human cultures. The other subfields are cultural anthropology that studies living cultures, physical anthropology that studies human biology and where humans fit among the living and extinct species of our family tree, and linguistics that studies human language.