1670s, "watery animal fluid," especially the clear pale-yellow liquid which separates in coagulation of blood in wounds, etc., from Latin serum "watery fluid, whey." This is held to be from PIE *sero- "flowing, liquid," from verbal root *ser- "to run, flow" (source also of Greek oros "whey, watery parts of curdled milk;" Sanskrit sarah "flowing, liquid," sarit "brook, river"). The word was applied by 1893 to blood serum used in medical treatments.
word-forming element meaning "a speaking, discourse, treatise, doctrine, theory, science," from Greek -logia (often via French -logie or Medieval Latin -logia), from -log-, combining form of legein "to speak, tell;" thus, "the character or deportment of one who speaks or treats of (a certain subject);" from PIE root *leg- (1) "to collect, gather," with derivatives meaning "to speak (to 'pick out words')." Often via Medieval Latin -logia, French -logie. In philology "love of learning; love of words or discourse," apology, doxology, analogy, trilogy, etc., Greek logos "word, speech, statement, discourse" is directly concerned.
<a href="https://www.etymonline.com/word/serology">Etymology of serology by etymonline</a>
Harper, D. (n.d.). Etymology of serology. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/serology