I am looking for mathematics textbooks on stochastic calculus. Any recommendation will be welcomed.

There are many but if you can define your interest and level it will cut down on the books to a more manageable level.For finance and in general ?Assuming what background in probability ? You should find many recommendations already in this Forum.

Four I like (from my Masters course) are:Oksendal - Stochastic Diff EquationsWilliams - Probability with MartingalesElementary Stochastic Calculus, with Finance in View: 6 (Advanced Series on Statistical Science & Applied Probability)Financial Calculus: An Introduction to Derivative Pricing - Baxter and RennieAll are good general introductions, Oksendal is the least financial and Baxter and Rennie the most.Links to all are The Williams book is the best book for the probability you'll need - it's pretty dense but if you stick with it, it's worth the effort! here

The Williams book looks pretty good. I am interested in the underlying mathematics. Thank you for the recommendation.QuoteOriginally posted by: RufusFour I like (from my Masters course) are:Oksendal - Stochastic Diff EquationsWilliams - Probability with MartingalesElementary Stochastic Calculus, with Finance in View: 6 (Advanced Series on Statistical Science & Applied Probability)Financial Calculus: An Introduction to Derivative Pricing - Baxter and RennieAll are good general introductions, Oksendal is the least financial and Baxter and Rennie the most.The Williams book is the best book for the probability you'll need - it's pretty dense but if you stick with it, it's worth the effort!

Apologies - links were broken, they are all hereQuoteOriginally posted by: RufusFour I like (from my Masters course) are:Oksendal - Stochastic Diff EquationsWilliams - Probability with MartingalesElementary Stochastic Calculus, with Finance in View: 6 (Advanced Series on Statistical Science & Applied Probability)Financial Calculus: An Introduction to Derivative Pricing - Baxter and RennieAll are good general introductions, Oksendal is the least financial and Baxter and Rennie the most.Links to all are The Williams book is the best book for the probability you'll need - it's pretty dense but if you stick with it, it's worth the effort! here

I have an extensive list with discussion on www.markjoshi.com

williams is a great book, but its not on stochastic calculus. its like a first course in graduate probability. i think oksendal is kind of bad at writing text books, but "SDE" is better than his other ones. karatzas and shreve is the most famous but it really kind of sucks. for pure math approaches, I think Protter (Stochastic Integration and Differential Equations), and Kallenberg (Foundations of Modern Probability) are the two best I've seen.

Most of the continuous time books assume that you already know the discrete times stuff, so you need to read Williams.

For discrete Pliska "Introduction to Mathematical Finance" and Follmer 'Stochastic Finance: An Introduction In Discrete Time.'An older book that is very good is Dothan 'Prices in Financial Markets.' Shreve's two volume Stochastic Calculus for FinanceVolume I: The Binomial Asset Pricing ModelVolume II: Continuous-Time Models are very good but more derivative oriented than the others.

An introduction to stochastic modeling by Karlin and Taylorone of the fist books that I used, it explains all concepts clearly.