inclusion-exclusion formula and Mobius inversion formula

Could any one explain to me what is the Mobius inversion formula and what is it connection with the principle of inclusion and exclusion?

My understanding is that Mobuis inversion formula can find the inverse of a function using algebraic subtraction/addition in a similar way as the inclusion-exclusion formula doing adding/subtraction.

if this is correct my next question is how do people find the Mobius inverse function?

• It just so happens that in an answer to this question someone just pointed me to the book A Course in Enumeration by Martin Aigner, in which Section $5.2$ explains the connection between Möbius inversion and inclusion-exclusion. (Note that the letters 'o' and 'ö', though graphically similar and historically related, stand for completely different phonemes, so replacing an 'ö' by an 'o' is about as bad a misspelling as, say, replacing an 'a' by an 'i'.) – joriki Jun 1 '16 at 14:17
• Many thanks for the reference. However, I do not have access to any library. Is it possible for you to summarize it? Furthermore, please comment on my point view, i.e. "Mobuis inversion formula can find the inverse of a function using algebraic subtraction/addition in a similar way as the inclusion-exclusion formula doing adding/subtraction." Is that correct? I understand Mobius is a Germany. However, my computer cannot type umlaub...should I type Moebius? – Quant Jun 3 '16 at 3:34