The main proofs are to be read from the following order -- Proofs are given here https://www.statlect.com/fundamentals-of-statistics/ It should be accompanied by the econometrics lecture given here and here
These can be accompanied by the following books
- Foundations of Statistics for Data Scientists R and Python by Agresti and Kateri
- Introductory Econometrics: A Modern Approach by Woodridge
For algorithmic treatment that talks about efficient mechanisms to optimize consult