Doctor, asthmatic, inviting me back for a subject to study (11)
I believe the answer is:
mathematics
'study' is the definition.
(mathematics is a kind of study)
'doctor asthmatic inviting me back' is the wordplay.
'doctor' indicates anagramming the letters.
'inviting' is an insertion indicator.
'back' says the letters should be written backwards.
'me' backwards is 'em'.
'asthmatic' anagrammed gives 'mathatics'.
'mathatics' going around 'em' is 'MATHEMATICS'.
'for a subject to' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for mathematics that I've seen before include "The science of numbers etc" , "a school subject" , "Numerical science" , "Sums" , "Number science" .)