Some confusion about definition of univalent function I was studying about univalent function from this pdf . But in this pdf, it is written that function is univalent if it is injective. But I have read many places that function is univalent if it is analytic and one one in given domain. So I am really confused whether I should read this pdf or not. Please guide.

The theory of "univalent functions" in complex analysis is all about univalent analytic functions. This particular author seems to want to separate the "injective" and "analytic" parts. I don't know why. So he might say that a function is "analytic and univalent" where someone else, for whom "analytic" is part of the definition of univalent, would just say "univalent". I don't know if he ever says anything about non-analytic one-to-one functions, which he might call "univalent", while the other author would just call it "injective".

But a little bit of terminological eccentricity is not a reason to discard the pdf.