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For general mathematical statistics concepts, OpenStax and the Open Textbook Library provide high-quality, peer-reviewed textbooks for free. Unbiasedness : (E_\theta[\hat\theta]=\theta)
Mathematical statistics is the branch of statistics that uses probability theory and rigorous mathematical reasoning to develop methods for collecting, analyzing, and interpreting data. While applied statistics focuses on the practical implementation of these methods, mathematical statistics supplies the theoretical underpinnings that guarantee their validity, optimality, and robustness. The discipline can be viewed as a bridge between pure probability theory and real‑world data analysis. "Mathematical Statistics" by P
The (L(\theta; x) = \prod_i=1^n f(x_i|\theta)) (or its log version) is the cornerstone for estimation and testing.