Yes, the first book in particular (Hull's "Options, Futures, and Other Derivatives") goes very slowly and introduces many of the financial concepts. It is a long book, around 1000 pages or so, whereas Baxter&Rennie ("Financial Calculus: An Introduction to Derivative Pricing") is something like 200, still keeping the mathematics at an informal level, akin to physics books. The last of the three bookes I listed, Oksendal ("Stochastic Differential Equations"), is for someone who has taken some math classes, and so starting from where the course in measure theory/probability left off, develops the machinery to deal with stochastic differential equations. If you wanted to start from a more elementary level and with a bit more finance than Oksendal, though still keeping the treatment quite rigorous, Shreve has a couple of books ("Stochastic Calculus for Finance I and II") you may find useful. Once you know the basics, then there's all the books, and there's a lot of them, on the specifics of different asset classes, e.g. Piterbarg&Andersen ("Interest Rate Modeling Vols I, II, II"). All of the books above are very much from the traditional stochastic calculus point of view.Thank you very much again!
I understood it better this time, however I seriously need to learn about all the concepts and ideas.
Are the first two books you recommended good for this (to learn about the names, the ideas, the institutions, more than the math)? I would start then with one of them, as well as an introductory book about statistics because I think there are more positions out there (also outside of finance) that use statistics. I have also searched for firms in finance or consulting that go in the direction of financial / risk modelling. Most of them demand statistics.
May I ask about your background? Are you working in that area?
Also as a word of caution, I advise against reading finance books written with a physics slant, such as Voit's "The Statistical Mechanics of Financial Markets". They may be of good general interest reading (in very rough terms, Voit's book is a more technical version of Sornette's "Why Stock Markets Crash", which in turn is a more technical version of Taleb's "Black Swan"), but often deal either more with economics than finance or otherwise focus on the "non-essential" when it comes to beneficial skills in the industry, or in the worst case can be misleading.
If you want something completely non-technical, Derman's "My Life as a Quant" and Das's "Traders, Gun & Money" are interesting, and Duhon's "How the Trading Floor Really Works" can give a picture what happens inside banks, and as always Michael Lewis's books are entertaining.
With that out of the way, I agree with others (and I knwo it can get a bit repetitive to hear this again and again) who've written here that it's a bit odd that you seem so set on quantitative finance, yet don't want to take formal studies in it. Also, software engineering is as of late similarly competitive to finance in terms of both compensation, and level of technical expertise required (think DeepMind etc), so if those things are important to you, as I infer from your messages, you might still want to reconsider what it is that you want to do.
I get the impression (because you mentioned consulting so many times) that someone told you to look into consulting and you accidentally happened upon the Big 4, and not the Big 3 that would probably be more typical for someone with a physics PhD, and you then found quantitative finance etc. as some of the services they provide. If you are looking at the postings at consultancies' websites, do know that they'd kind of only ever get hired to do technical work if the non-core workload becomes too much for in-house resources to handle, often due to regulatory pressure (so obviously this is for banks; I've never heard of hedge funds hiring quants in a consulting capacity, and would find it quite odd if they did), and so they also would typically get offloaded with some of the least interesting bits that are nevertheless important to deliver.