immunology n.

mid-15c., "free, exempt" (from taxes, tithes, sin, etc.), from Latin immunis "exempt from public service, untaxed; unburdened, not tributary," literally "not paying a share," from assimilated form of in- "not, opposite of" (see in- (1)) + munis "performing services" (compare municipal), from PIE *moi-n-es-, suffixed form of root *mei- (1) "to change, go, move." Specific modern medical sense of "exempt (from a disease)," typically because of inoculation, is from 1881, a back-formation from immunity. Immune system attested by 1917.

word-forming element indicating "branch of knowledge, science," now the usual form of -logy. Originally used c. 1800 in nonce formations (commonsensology, etc.), it gained legitimacy by influence of the proper formation in geology, mythology, etc., where the -o- is a stem vowel in the previous element.

The second element is prop[erly] -logy (-logue, etc.), the -o- belonging to the preceding element; but the accent makes the apparent element in E[nglish] to be -ology, which is hence often used as an independent word. [Century Dictionary]