If you come from a pure math theory first background I would advise starting out with Björks “Arbitrage theory in continuous time”, I personally found the lack of rigor and superfluous examples in Hull frustrating and found Björk much more approachable then you can look into Hull for real life practicalities like daycount conventions, etc. If you want to go into complex derivatives pricing I would advise looking at the Andersen and Piterbarg trilogy.
I would also suggest to forget about Hull and Wilmott and would suggest to start with the excellent book by Shreve: "Stochastic Calculus for Finance. Volume II: Continuous Time Models".
Then, you can quickly read Bjoerk, work through Brigo/Mercurio (if you like that style) or Andersen/Piterbarg. Alternatively, if you want to fully dive into into the subject after Shreve, Musiela/Rutkowski: "Martingale Methods in Financial Modelling" is wonderful.
I'd say that Shreve and Musiela lack rigour and are too focused on trivia, name-dropping and anecdotes. Jiao's "Infinite-dimensional methods in amassing vast bags of gold" is unsurpassed. For its coverage of Black-Scholes, I'd also recommend Schulz's "Good Grief, Charlie Brown". Sorry, everyone seemed to be doing this so I felt I should contribute too.
