
Algorithmic Trading & DMA by Barry Johnson
Trading and Exchanges: Market Microstructure for Practitioners by Larry Harris
You might also be interested in 'yummyfajitas blog:
https://www.chrisstucchio.com/blog/2012/hft_apology.html
If people have up to date replacements for these books, I'd be super interested.
If you keep asking around, people are gunnuh recommend Reminiscences of a Stock Operator, and it's an enjoyable book but keep in mind that it's basically the fictionalized biography of a problem gambler who happened to operate in the stock market, he traded recklessly and died destitute (by suicide - when you reread it, you start to notice how he never mentions enjoying anything, or talks about the people in his life in more than passing). Don't take it too seriously.
The book is kind of old now, but it was written by Barry Johnson, who worked at Morgan Stanley on their algo trading team.
The book is kind of dry, but very thorough and clear on its concepts. It reads more like a university text book than anything else. It just goes through concepts one by one, chapter by chapter.
[0]: https://www.amazon.co.uk/Algorithmic-Trading-DMA-introductio...
Trading and Exchanges: Market Microstructure for Practitioners (cost of this on Amazon seems to have more than doubled since I bought it 11 years ago)
Algorithmic Trading and DMA: An introduction to direct access trading strategies
This is a bit separate from the actual execution in the market, which is called smart order routing, and that just focuses on speed.
The best book on this still seems to be the now almost 10 year old "Algorithmic Trading and DMA" by Barry Johnson. If you want to get a feel for the strategies involved, this is your best bet: https://www.amazon.com/Algorithmic-Trading-DMA-introduction-...
As for job titles, they tend to be generic like "infrastructure developer, strategist" but look for key words like "Smart Order Router, Algorithmic Trading, Index Arb (itrage), statistical arbitrage, market making, dark pool. I put two of those in Morgan Stanley's site and got a bunch of relevant hits. Posting numbers 3119617 3120636 are actual jobs in this space.
A better bet is to just look at job openings for the companies who specialize in this stuff- Virtu, Jump, Hudson River Trading, Citadel Securities, etc...
Read Options, Futures and Other Derivatives and Algorithmic Trading and DMA and you basically know everything you'll get from public sources that could be meaningful for trading.
If he knows how to code and is looking for "mathematics of finance" he should start with those, not the CFA.
Algorithmic Trading & DMA by Johnson
Both are dated now but still good foundational books.