I definitely recommand "Introduction to Stochastic Calculus Applied to Finance" by Lamberton and Lapeyre. It is concise, precise, introduce all the mathematics you want by constructing the Ito calculus, the Black-Scholes model, formulation of the pricing via martingales and PDE, some interest rate theory and then introducing jumps and finishing by the algorithmic side. Then you can read "The Concepts and Practice of Mathematical Finance " by Mark Joshi where you can gain more insight on the financial side and the technics used by the practionners. I think this could be a good start.

There is also the excellent lectures by Emmanuel Derman that you can find here http://www.ederman.com/new/docs/laughter.html. You can read theme even before the Joshi book. It goes from the basics to local-stochastic volatility in a physicist spirit with lot of intuition

I definitely recommand "Introduction to Stochastic Calculus Applied to Finance" by Lamberton and Lapeyre. It is concise, precise, introduce all the mathematics you want by constructing the Ito calculus, the Black-Scholes model, formulation of the pricing via martingales and PDE, some interest rate theory and then introducing jumps and finishing by the algorithmic side. Then you can read "The Concepts and Practice of Mathematical Finance " by Mark Joshi where you can gain more insight on the financial side and the technics used by the practionners. I think this could be a good start.