The primary goal of this survey is to provide a thorough overview of fairness measures and biases in machine learning and their optimization for reducing bias in protected classes, specifically concerning demographic data. The surveyed fairness measures include demographic parity, disparate impact, equalized odds, equal opportunity, and statistical parity difference. We also explore how these measures are optimized for multi-class cases. The survey also addresses discrimination types such as disparate impact, disparate mistreatment, and disparate treatment. Various biases, including confirmation bias, population bias, sampling/selection bias, interaction bias, decline bias, hindsight bias, in-group bias, emergent bias, label bias, and outcome proxy bias are covered. The scope of the survey extends to topics such as the Dunning-Kruger effect and Simpson’s paradox. The exploration digs into Fair Classification, Fair Clustering, and Fair Regression, exploring algorithms that contribute to ensuring fairness across different areas of machine learning and optimization processes.