Textbook/resources for a beginning researcher in (Machine) Learning Theory
People are going to recommend

http://www.cs.nyu.edu/~mohri/mlbook/

and

http://www.cs.huji.ac.il/~shais/UnderstandingMachineLearning/understanding-machine-learning-theory-algorithms.pdf

-- so I might as well do it first :)

I still think the Anthony-Bartlett is a better start for the mathematically oriented beginner.